Edit Profile Takhtajan, Leon Armenovich Compute Distance To: Compute Author ID: takhtajan.leon-a Published as: Takhtadzhyan, L. A.; Takhtajan, Leon A.; Takhtajan, L. A.; Takhtajan, Leon; Takhtadzhan, L. A.; Tahtadzjan, L. A.; Takhtadzhyan, L.; Takhtajan, L. Homepage: http://www.math.stonybrook.edu/~leontak/ External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 113 Publications since 1973, including 10 Books all top 5 Co-Authors 35 single-authored 18 Faddeev, Lyudvig Dmitrievich 15 Zograf, P. G. 13 Vinogradov, Askol’d Ivanovich 5 Reshetikhin, Nikolai Yu. 5 Teo, Lee-Peng 4 Aref’eva, Irina Yaroslavna 4 4 Sklyanin, Evgeny K. 3 Ablowitz, Mark Jay 3 Ge, Molin 3 Niemi, Antti J. 3 Phua, Kok Khoo 3 Shatashvili, Samson L. 3 Zakharov, Vladimir Evgen’evich 3 Zograf, Peter 2 Aldrovandi, Ettore 2 Kozlov, Valeriĭ Vasil’evich 2 Laptev, Ari 2 Maslov, Viktor Pavlovich 2 Novikov, Sergeĭ Petrovich 2 Polyakov, Aleksandr Markovich 2 Schimmer, Lukas 2 Smirnov, Fedor A. 2 Venkov, Alexei Borisovich 1 Alekseev, Anton Yu. 1 Bukhshtaber, Viktor Matveevich 1 Buslaev, Vladimir Savel’evich 1 Chakravarty, Sarbarish 1 Chatterjee, Rupak 1 Dalets’kyĭ, Yuriĭ L’vovych 1 Dito, Giuseppe 1 Flato, Moshé 1 Fortov, Vladimir E. 1 Franchini, Fabio 1 Ibragimov, Il’dar Abdullovich 1 Its, Alexander Rudolfovich 1 Keiser, James M. 1 Kislyakov, Sergeĭ Vital’evich 1 Korepin, Vladimir E. 1 Krichever, Igor’ Moiseevich 1 Kulish, Petr Petrovich 1 Lipatov, Lev N. 1 Lyubich, Mikhail Yur’evich 1 Mcintyre, Andrew 1 Meneses, Cláudio N. 1 Osipov, Yuriĭ Sergeevich 1 Park, Jinsung 1 Rubakov, Valery A. 1 Simonov, Yuri A. 1 Sinaĭ, Yakov Grigor’evich 1 Sokolov, I. A. 1 Sternheimer, Daniel 1 Velikhov, E. P. 1 Zhizhchenko, Alexey B. all top 5 Serials 9 Communications in Mathematical Physics 9 Journal of Soviet Mathematics 9 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 6 Letters in Mathematical Physics 5 Russian Mathematical Surveys 4 Theoretical and Mathematical Physics 3 Modern Physics Letters A 3 Functional Analysis and its Applications 3 Mathematische Annalen 3 Soviet Mathematics. Doklady 3 Proceedings of the Steklov Institute of Mathematics 2 Matematicheskiĭ Sbornik. Novaya Seriya 2 Physica D 2 Geometric and Functional Analysis. GAFA 2 Mathematics of the USSR, Sbornik 2 Izvestiya: Mathematics 1 Journal of Mathematical Physics 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Reviews in Mathematical Physics 1 Journal of Geometry and Physics 1 Advances in Mathematics 1 Geometriae Dedicata 1 Journal für die Reine und Angewandte Mathematik 1 Mathematics of the USSR. Izvestiya 1 Memoirs of the American Mathematical Society 1 Quaestiones Mathematicae 1 Transactions of the American Mathematical Society 1 Leningrad Mathematical Journal 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Soviet Physics. Doklady 1 St. Petersburg Mathematical Journal 1 European Mathematical Society Newsletter 1 Quantum Information Processing 1 Graduate Studies in Mathematics 1 Proceedings of Symposia in Pure Mathematics 1 Trudy Matematicheskogo Instituta Imeni V. A. Steklova 1 Classics in Mathematics all top 5 Fields 44 Quantum theory (81-XX) 32 Several complex variables and analytic spaces (32-XX) 22 Partial differential equations (35-XX) 20 Dynamical systems and ergodic theory (37-XX) 19 Number theory (11-XX) 19 Functions of a complex variable (30-XX) 17 Differential geometry (53-XX) 16 Algebraic geometry (14-XX) 15 Global analysis, analysis on manifolds (58-XX) 11 Nonassociative rings and algebras (17-XX) 9 Mechanics of particles and systems (70-XX) 8 Associative rings and algebras (16-XX) 7 Operator theory (47-XX) 6 History and biography (01-XX) 5 General and overarching topics; collections (00-XX) 5 Statistical mechanics, structure of matter (82-XX) 3 Difference and functional equations (39-XX) 3 Relativity and gravitational theory (83-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Topological groups, Lie groups (22-XX) 2 Special functions (33-XX) 2 Ordinary differential equations (34-XX) 1 Category theory; homological algebra (18-XX) 1 \(K\)-theory (19-XX) 1 Group theory and generalizations (20-XX) 1 Potential theory (31-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 91 Publications have been cited 2,139 times in 1,832 Documents Cited by ▼ Year ▼ Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman. Reprint of the 1987 original. Zbl 1111.37001Faddeev, Ludwig D.; Takhtajan, Leon A. 285 2007 Quantization of Lie groups and Lie algebras. Zbl 0715.17015Reshetikhin, N. Yu.; Takhtadzhyan, L. A.; Faddeev, L. D. 260 1990 On foundation of the generalized Nambu mechanics. Zbl 0808.70015Takhtajan, Leon 189 1994 Quantum inverse problem method. I. Zbl 1138.37331Sklyanin, E. K.; Takhtadzhyan, L. A.; Faddeev, L. D. 164 1980 The spectral theory of a functional-difference operator in conformal field theory. Zbl 1327.39013Takhtajan, L. A.; Faddeev, L. D. 143 2015 Hamiltonian methods in the theory of solitons. (Гамил’тонов подход в теории солитонов.) Zbl 0632.58003Takhtadzhyan, L. A.; Faddeev, L. D. 119 1986 Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman. Zbl 0632.58004Faddeev, L. D.; Takhtadzhyan, L. A. 67 1987 Weil-Petersson metric on the universal Teichmüller space. Zbl 1243.32010Takhtajan, Leon A.; Teo, Lee-Peng 65 2006 Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model. Zbl 0532.47009Faddeev, L. D.; Takhtadzhyan, L. A. 55 1984 Quantization of Lie groups and Lie algebras. Zbl 0677.17010Faddeev, L. D.; Reshetikhin, N. Yu.; Takhtadzhan, L. A. 51 1989 Leibniz and Lie algebra structures for Nambu algebra. Zbl 0869.58024Daletskii, Yuri L.; Takhtajan, Leon A. 49 1997 On uniformization of Riemann surfaces and the Weil-Petersson metric on Teichmüller and Schottky spaces. Zbl 0663.32017Zograf, P. G.; Takhtadzhyan, L. A. 35 1988 A self-dual Yang-Mills hierarchy and its reductions to integrable systems in \(1+1\) and \(2+1\) dimensions. Zbl 0795.58027Ablowitz, Mark J.; Chakravarty, Sarbarish; Takhtajan, Leon A. 34 1993 Quantum mechanics for mathematicians. Zbl 1156.81004Takhtajan, Leon A. 32 2008 A local index theorem for families of \({\bar \partial}\)-operators on punctured Riemann surfaces and a new Kähler metric on their moduli spaces. Zbl 0725.58043Takhtadzhyan, L. A.; Zograf, P. G. 30 1991 Essentially nonlinear one-dimensional model of classical field theory. Zbl 0299.35063Tahtadzjan, L. A.; Faddeev, L. D. 30 1975 Deformation quantization and Nambu mechanics. Zbl 0877.70012Dito, G.; Flato, M.; Sternheimer, D.; Takhtajan, L. 28 1997 Liouville action and Weil-Petersson metric on deformation spaces, global Kleinian reciprocity and holography. Zbl 1065.30046Takhtajan, Leon A.; Teo, Lee-Peng 25 2003 Complete description of solutions of the ’sine-Gordon’ equation. Zbl 0312.35051Zakharov, V. E.; Takhtadzhyan, L. A.; Faddeev, L. D. 24 1974 Hyperbolic \(2\)-spheres with conical singularities, accessory parameters and Kähler metrics on \({\mathcal{M}}_{0,n}\). Zbl 1075.32006Takhtajan, Leon; Zograf, Peter 22 2003 On Liouville’s equation, accessory parameters, and the geometry of Teichmüller space for Riemann surfaces of genus 0. Zbl 0655.32022Zograf, P. G.; Takhtadzhyan, L. A. 22 1988 The quantum inverse problem method. I. Zbl 0449.35096Faddeev, L. D.; Sklyanin, E. K.; Takhtadzhyan, L. A. 19 1979 Holomorphic factorization of determinants of Laplacians on Riemann surfaces and a higher genus generalization of Kronecker’s first limit formula. Zbl 1110.58026McIntyre, A.; Takhtajan, L. A. 18 2006 Deformation quantization of Kähler manifolds. Zbl 1003.53061Reshetikhin, N.; Takhtajan, L. A. 17 2000 Weyl type asymptotics and bounds for the eigenvalues of functional-difference operators for mirror curves. Zbl 1361.47004Laptev, Ari; Schimmer, Lukas; Takhtajan, Leon A. 17 2016 Aspects of classical and quantum Nambu mechanics. Zbl 0861.70018Chatterjee, Rupak; Takhtajan, Leon 14 1996 Topics in the quantum geometry of Riemann surfaces: Two-dimensional quantum gravity. Zbl 0919.17022Takhtajan, L. A. 14 1996 Free bosons and tau-functions for compact Riemann surfaces and closed smooth Jordan curves. Current correlation functions. Zbl 1072.14521Takhtajan, Leon A. 13 2001 The spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model. Zbl 0471.47009Takhtadzhyan, L. A.; Faddeev, L. D. 12 1981 The zeta-function of the additive divisor problem and the spectral expansion of the automorphic Laplacian. Zbl 0536.10025Vinogradov, A. I.; Takhtadzhyan, L. A. 12 1984 Theory of Eisenstein series for the group SL(3,R) and its application to a binary problem. Zbl 0476.10024Vinogradov, A. I.; Takhtadzhyan, L. A. 11 1982 Theory of Eisenstein series for the group \(\mathrm{SL}(3,\mathbb{R})\) and its application to a binary problem. I: Fourier expansion of the highest Eisenstein series. Zbl 0434.10020Vinogradov, A. I.; Takhtadzhyan, L. A. 11 1978 Scattering theory for the Korteweg-de Vries (KdV) equation and its Hamiltonian interpretation. Zbl 0618.35100Buslaev, V. S.; Faddeev, L. D.; Takhtadzhan, L. A. 11 1986 On uniformization of Riemann surfaces and the Weil-Petersson metric on Teichmüller and Schottky spaces. Zbl 0642.32011Zograf, P. G.; Takhtadzhyan, L. A. 11 1987 Liouville theory: Quantum geometry of Riemann surfaces. Zbl 1021.81891Takhtajan, Leon A. 10 1993 Elementary introduction to quantum groups. Zbl 0820.17013Takhtajan, L. A. 10 1993 A local index theorem for families of \(\overline{\partial}\)-operators on Riemann surfaces. Zbl 0659.58043Zograf, P. G.; Takhtadzhyan, L. A. 10 1987 The Selberg zeta function and a new Kähler metric on the moduli space of punctured Riemann surfaces. Zbl 0739.30032Takhtadzhyan, L. A.; Zograf, P. G. 9 1988 Poisson structure for the KdV equation. Zbl 0595.35093Faddeev, L. D.; Takhtadzhan, L. A. 9 1985 On Liouville equations, accessory parameters, and the geometry of Teichmüller spaces for Riemann surfaces of genus 0. Zbl 0642.32010Zograf, P. G.; Takhtadzhyan, L. A. 9 1987 Noncommutative homology of quantum tori. Zbl 0708.19003Takhtadzhyan, L. A. 8 1989 On Bott-Chern forms and their applications. Zbl 1303.32014Pingali, Vamsi P.; Takhtajan, Leon A. 8 2014 A local index theorem for families of \({\bar \partial}\)-operators on Riemann surfaces. Zbl 0699.58061Zograf, P. G.; Takhtadzhyan, L. A. 8 1987 Equivalence of geometric \(h<1/2\) and standard \(c>25\) approaches to two-dimensional quantum gravity. Zbl 1022.81750Takhtajan, Leon A. 7 1996 The first Chern form on moduli of parabolic bundles. Zbl 1156.14028Takhtajan, Leon A.; Zograf, Peter 7 2008 Quantum Liouville theory in the background field formalism. I: Compact Riemann surfaces. Zbl 1114.32007Takhtajan, Leon A.; Teo, Lee-Peng 6 2006 Semi-classical Liouville theory, complex geometry of moduli spaces, and uniformization of Riemann surfaces. Zbl 1221.32006Takhtajan, Leon 6 1992 On the Linnik-Skubenko asymptotics. Zbl 0488.10017Vinogradov, A. I.; Takhtadzhyan, L. A. 6 1980 On the geometry of moduli spaces of vector bundles over a Riemann surface. Zbl 0689.53037Zograf, P. G.; Takhtadzhyan, L. A. 6 1989 Local index theorem for orbifold Riemann surfaces. Zbl 1417.58024Takhtajan, Leon A.; Zograf, Peter 6 2019 On analogues of the Vinogradov-Gauss formula. Zbl 0468.10022Vinogradov, A. I.; Takhtadzhyan, L. A. 5 1980 Analogues of the Gauss-Vinogradov formula on the critical line. Zbl 0468.10023Takhtadzhyan, L. A.; Vinogradov, A. I. 5 1981 Modular forms as \(\tau\)-functions for certain integrable reductions of the Yang-Mills equations. Zbl 0814.35110Takhtajan, Leon A. 5 1993 The Hamiltonian system connected with the equation u//(xi,nu)+sin u=0. Zbl 0412.35065Takhtadzhyan, L. A.; Faddeev, L. D. 5 1976 Potentials and Chern forms for Weil-Petersson and Takhtajan-Zograf metrics on moduli spaces. Zbl 1353.14044Park, Jinsung; Takhtajan, Leon A.; Teo, Lee-Peng 5 2017 Generating functional in CFT and effective action for two-dimensional quantum gravity on higher genus Riemann surfaces. Zbl 0998.81097Aldrovandi, Ettore; Takhtajan, Leon A. 5 1997 Action of the Liouville equation is a generating function for the accessory parameters and the potential of the Weil-Petersson metric on the Teichmüller space. Zbl 0612.32018Zograf, P. G.; Takhtadzhyan, L. A. 5 1985 Liouville theory: Ward identities for generating functional and modular geometry. Zbl 1021.81892Takhtajan, Leon A. 4 1994 Introduction to quantum groups. Zbl 0735.17009Takhtadzhyan, L. A. 4 1990 A higher order analog of the Chevalley-Eilenberg complex and the deformation theory of \(n\)-gebras. Zbl 0833.17021Takhtajan, L. A. 4 1994 Self-dual Yang-Mills equation and new special functions in integrable systems. Zbl 0941.37542Chakravarty, S.; Ablowitz, M. J.; Takhtajan, L. A. 4 1992 Analogues of the Gauss-Vinogradov formula on the critical line. Zbl 0534.10039Vinogradov, A. I.; Takhtadzhyan, L. A. 4 1984 Uniformization, local index theorem, and geometry of the moduli spaces of Riemann surfaces and vector bundles. Zbl 0689.30035Takhtajan, L. A. 4 1989 Spectrum of the density matrix of a large block of spins of the \(XY\) model in one dimension. Zbl 1216.81027Franchini, F.; Its, A. R.; Korepin, V. E.; Takhtajan, L. A. 3 2011 On the geometry of moduli spaces of vector bundles over a Riemann surface. Zbl 0715.53048Zograf, P. G.; Takhtadzhyan, L. A. 3 1990 Scientific heritage of L. D. Faddeev. Survey of papers. Zbl 1396.81008Takhtajan, Leon A.; Alekseev, Anton Yu.; Aref’eva, Irina Ya.; Semenov-Tian-Shansky, Michael A.; Sklyanin, Evgeny K.; Smirnov, Fedor A.; Shatashvili, Samson L. 3 2017 The quantum inverse problem method and the XYZ Heisenberg model. Zbl 1194.81247Takhtajan, Leon A. 3 1981 Solutions of the triangle equations with \({\mathbb{Z}}_ n\times {\mathbb{Z}}_ n\)-symmetry and matrix analogues of the Weierstrass zeta- and sigma- functions. Zbl 0542.15003Takhtadzhyan, L. A. 3 1984 Analogs of the Vinogradov-Gauss formula in the critical strip. Zbl 0483.12002Vinogradov, A. I.; Takhtadzhyan, L. A. 2 1981 The Gauss-Hasse hypothesis on real quadratic fields with class number one. Zbl 0497.12004Takhtadzhan, L. A.; Vinogradov, A. I. 2 1982 Stable, multi-state, time-reversible cellular automata with rich particle content. Zbl 0787.58022Ablowitz, M. J.; Keiser, J. M.; Takhtadzhyan, L. A. 2 1992 Generating functional in CFT on Riemann surfaces II: Homological aspects. Zbl 1024.81036Aldrovandi, Ettore; Takhtajan, Leon A. 2 2002 Weil-Petersson geometry of the universal Teichmüller space. Zbl 1142.32300Takhtajan, Leon A.; Teo, Lee-Peng 2 2005 Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations. Zbl 0562.35088Takhtadzhyan, L. A.; Faddeev, L. D. 2 1985 Integrable models in classical and quantum field theory. Zbl 0569.47010Takhtajan, L. A. 2 1984 The zeta-function of the additive divisor problem and spectral decomposition of the automorphic Laplacian. Zbl 0609.10023Vinogradov, A. I.; Takhtadzhyan, L. A. 2 1987 Quantum field theories on an algebraic curve. Zbl 1024.81016Takhtajan, Leon A. 1 2000 Quantum groups. Zbl 0716.17010Faddeev, L.; Reshetikhin, N.; Takhtadzhyan, L. 1 1989 A simple connection between geometric and Hamiltonian representations of integrable nonlinear equations. Zbl 0505.35082Takhtadzhyan, L. A.; Faddeev, L. D. 1 1982 Potential of the Weil-Petersson metric on the Torelli space. Zbl 0900.32007Zograf, P. G.; Takhtadzhyan, L. A. 1 1987 Integrable cellular automata and AKNS hierarchy. Zbl 0860.35117Takhtajan, Leon A. 1 1996 A simple example of modular forms as tau-functions for integrable equations. Zbl 0794.35114Takhtadzhyan, L. A. 1 1992 Hamiltonian systems connected with the Dirac equation. Zbl 0404.35087Tahtadzjan, L. A. 1 1977 Asymptotic formula for the sum of the lengths of the periods of the quadratic irrationalities of discriminant D. Zbl 0442.10007Takhtadzhyan, L. A. 1 1979 Ludwig Faddeev memorial volume. A life in mathematical physics. Zbl 1398.81011Ge, Mo-Lin (ed.); Niemi, Antti J. (ed.); Phua, Kok Khoo (ed.); Takhtajan, Leon A. (ed.) 1 2018 An estimate of the residue of Rankin L-series. Zbl 0516.10017Vinogradov, A. I.; Takhtadzhyan, L. A. 1 1982 Analogues of the Vinogradov-Gauss formula in the critical strip. Zbl 0523.12011Vinogradov, A. I.; Takhtadzhyan, L. A. 1 1983 The potential of the Weil-Petersson metric on Torelli space. Zbl 0631.32020Zograf, P. G.; Takhtadzhyan, L. A. 1 1987 Weyl asymptotics for perturbed functional difference operators. Zbl 1427.81063Laptev, Ari; Schimmer, Lukas; Takhtajan, Leon A. 1 2019 Ludvig Dmitrievich Faddeev (on his 80th birthday). Zbl 1311.01030Aref’eva, I. Ya.; Buchstaber, V. M.; Velikhov, E. P.; Zhizhchenko, A. B.; Zakharov, V. E.; Ibragimov, I. A.; Kislyakov, S. V.; Kozlov, V. V.; Kulish, P. P.; Lipatov, L. N.; Maslov, V. P.; Matveev, V. A.; Novikov, S. P.; Osipov, Yu. S.; Polyakov, A. M.; Rubakov, V. A.; Semenov-Tian-Shansky, M. A.; Simonov, Yu. A.; Sinai, Ya. G.; Slavnov, A. A.; Sokolov, I. A.; Takhtajan, L. A.; Fortov, V. E.; Shatashvili, S. L. 1 2014 Explicit computation of the Chern character forms. Zbl 1355.32016Takhtajan, Leon A. 1 2016 Local index theorem for orbifold Riemann surfaces. Zbl 1417.58024Takhtajan, Leon A.; Zograf, Peter 6 2019 Weyl asymptotics for perturbed functional difference operators. Zbl 1427.81063Laptev, Ari; Schimmer, Lukas; Takhtajan, Leon A. 1 2019 Ludwig Faddeev memorial volume. A life in mathematical physics. Zbl 1398.81011Ge, Mo-Lin; Niemi, Antti J.; Phua, Kok Khoo; Takhtajan, Leon A. 1 2018 Potentials and Chern forms for Weil-Petersson and Takhtajan-Zograf metrics on moduli spaces. Zbl 1353.14044Park, Jinsung; Takhtajan, Leon A.; Teo, Lee-Peng 5 2017 Scientific heritage of L. D. Faddeev. Survey of papers. Zbl 1396.81008Takhtajan, Leon A.; Alekseev, Anton Yu.; Aref’eva, Irina Ya.; Semenov-Tian-Shansky, Michael A.; Sklyanin, Evgeny K.; Smirnov, Fedor A.; Shatashvili, Samson L. 3 2017 Weyl type asymptotics and bounds for the eigenvalues of functional-difference operators for mirror curves. Zbl 1361.47004Laptev, Ari; Schimmer, Lukas; Takhtajan, Leon A. 17 2016 Explicit computation of the Chern character forms. Zbl 1355.32016Takhtajan, Leon A. 1 2016 The spectral theory of a functional-difference operator in conformal field theory. Zbl 1327.39013Takhtajan, L. A.; Faddeev, L. D. 143 2015 On Bott-Chern forms and their applications. Zbl 1303.32014Pingali, Vamsi P.; Takhtajan, Leon A. 8 2014 Ludvig Dmitrievich Faddeev (on his 80th birthday). Zbl 1311.01030Aref’eva, I. Ya.; Buchstaber, V. M.; Velikhov, E. P.; Zhizhchenko, A. B.; Zakharov, V. E.; Ibragimov, I. A.; Kislyakov, S. V.; Kozlov, V. V.; Kulish, P. P.; Lipatov, L. N.; Maslov, V. P.; Matveev, V. A.; Novikov, S. P.; Osipov, Yu. S.; Polyakov, A. M.; Rubakov, V. A.; Semenov-Tian-Shansky, M. A.; Simonov, Yu. A.; Sinai, Ya. G.; Slavnov, A. A.; Sokolov, I. A.; Takhtajan, L. A.; Fortov, V. E.; Shatashvili, S. L. 1 2014 Spectrum of the density matrix of a large block of spins of the \(XY\) model in one dimension. Zbl 1216.81027Franchini, F.; Its, A. R.; Korepin, V. E.; Takhtajan, L. A. 3 2011 Quantum mechanics for mathematicians. Zbl 1156.81004Takhtajan, Leon A. 32 2008 The first Chern form on moduli of parabolic bundles. Zbl 1156.14028Takhtajan, Leon A.; Zograf, Peter 7 2008 Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman. Reprint of the 1987 original. Zbl 1111.37001Faddeev, Ludwig D.; Takhtajan, Leon A. 285 2007 Weil-Petersson metric on the universal Teichmüller space. Zbl 1243.32010Takhtajan, Leon A.; Teo, Lee-Peng 65 2006 Holomorphic factorization of determinants of Laplacians on Riemann surfaces and a higher genus generalization of Kronecker’s first limit formula. Zbl 1110.58026McIntyre, A.; Takhtajan, L. A. 18 2006 Quantum Liouville theory in the background field formalism. I: Compact Riemann surfaces. Zbl 1114.32007Takhtajan, Leon A.; Teo, Lee-Peng 6 2006 Weil-Petersson geometry of the universal Teichmüller space. Zbl 1142.32300Takhtajan, Leon A.; Teo, Lee-Peng 2 2005 Liouville action and Weil-Petersson metric on deformation spaces, global Kleinian reciprocity and holography. Zbl 1065.30046Takhtajan, Leon A.; Teo, Lee-Peng 25 2003 Hyperbolic \(2\)-spheres with conical singularities, accessory parameters and Kähler metrics on \({\mathcal{M}}_{0,n}\). Zbl 1075.32006Takhtajan, Leon; Zograf, Peter 22 2003 Generating functional in CFT on Riemann surfaces II: Homological aspects. Zbl 1024.81036Aldrovandi, Ettore; Takhtajan, Leon A. 2 2002 Free bosons and tau-functions for compact Riemann surfaces and closed smooth Jordan curves. Current correlation functions. Zbl 1072.14521Takhtajan, Leon A. 13 2001 Deformation quantization of Kähler manifolds. Zbl 1003.53061Reshetikhin, N.; Takhtajan, L. A. 17 2000 Quantum field theories on an algebraic curve. Zbl 1024.81016Takhtajan, Leon A. 1 2000 Leibniz and Lie algebra structures for Nambu algebra. Zbl 0869.58024Daletskii, Yuri L.; Takhtajan, Leon A. 49 1997 Deformation quantization and Nambu mechanics. Zbl 0877.70012Dito, G.; Flato, M.; Sternheimer, D.; Takhtajan, L. 28 1997 Generating functional in CFT and effective action for two-dimensional quantum gravity on higher genus Riemann surfaces. Zbl 0998.81097Aldrovandi, Ettore; Takhtajan, Leon A. 5 1997 Aspects of classical and quantum Nambu mechanics. Zbl 0861.70018Chatterjee, Rupak; Takhtajan, Leon 14 1996 Topics in the quantum geometry of Riemann surfaces: Two-dimensional quantum gravity. Zbl 0919.17022Takhtajan, L. A. 14 1996 Equivalence of geometric \(h<1/2\) and standard \(c>25\) approaches to two-dimensional quantum gravity. Zbl 1022.81750Takhtajan, Leon A. 7 1996 Integrable cellular automata and AKNS hierarchy. Zbl 0860.35117Takhtajan, Leon A. 1 1996 On foundation of the generalized Nambu mechanics. Zbl 0808.70015Takhtajan, Leon 189 1994 Liouville theory: Ward identities for generating functional and modular geometry. Zbl 1021.81892Takhtajan, Leon A. 4 1994 A higher order analog of the Chevalley-Eilenberg complex and the deformation theory of \(n\)-gebras. Zbl 0833.17021Takhtajan, L. A. 4 1994 A self-dual Yang-Mills hierarchy and its reductions to integrable systems in \(1+1\) and \(2+1\) dimensions. Zbl 0795.58027Ablowitz, Mark J.; Chakravarty, Sarbarish; Takhtajan, Leon A. 34 1993 Liouville theory: Quantum geometry of Riemann surfaces. Zbl 1021.81891Takhtajan, Leon A. 10 1993 Elementary introduction to quantum groups. Zbl 0820.17013Takhtajan, L. A. 10 1993 Modular forms as \(\tau\)-functions for certain integrable reductions of the Yang-Mills equations. Zbl 0814.35110Takhtajan, Leon A. 5 1993 Semi-classical Liouville theory, complex geometry of moduli spaces, and uniformization of Riemann surfaces. Zbl 1221.32006Takhtajan, Leon 6 1992 Self-dual Yang-Mills equation and new special functions in integrable systems. Zbl 0941.37542Chakravarty, S.; Ablowitz, M. J.; Takhtajan, L. A. 4 1992 Stable, multi-state, time-reversible cellular automata with rich particle content. Zbl 0787.58022Ablowitz, M. J.; Keiser, J. M.; Takhtadzhyan, L. A. 2 1992 A simple example of modular forms as tau-functions for integrable equations. Zbl 0794.35114Takhtadzhyan, L. A. 1 1992 A local index theorem for families of \({\bar \partial}\)-operators on punctured Riemann surfaces and a new Kähler metric on their moduli spaces. Zbl 0725.58043Takhtadzhyan, L. A.; Zograf, P. G. 30 1991 Quantization of Lie groups and Lie algebras. Zbl 0715.17015Reshetikhin, N. Yu.; Takhtadzhyan, L. A.; Faddeev, L. D. 260 1990 Introduction to quantum groups. Zbl 0735.17009Takhtadzhyan, L. A. 4 1990 On the geometry of moduli spaces of vector bundles over a Riemann surface. Zbl 0715.53048Zograf, P. G.; Takhtadzhyan, L. A. 3 1990 Quantization of Lie groups and Lie algebras. Zbl 0677.17010Faddeev, L. D.; Reshetikhin, N. Yu.; Takhtadzhan, L. A. 51 1989 Noncommutative homology of quantum tori. Zbl 0708.19003Takhtadzhyan, L. A. 8 1989 On the geometry of moduli spaces of vector bundles over a Riemann surface. Zbl 0689.53037Zograf, P. G.; Takhtadzhyan, L. A. 6 1989 Uniformization, local index theorem, and geometry of the moduli spaces of Riemann surfaces and vector bundles. Zbl 0689.30035Takhtajan, L. A. 4 1989 Quantum groups. Zbl 0716.17010Faddeev, L.; Reshetikhin, N.; Takhtadzhyan, L. 1 1989 On uniformization of Riemann surfaces and the Weil-Petersson metric on Teichmüller and Schottky spaces. Zbl 0663.32017Zograf, P. G.; Takhtadzhyan, L. A. 35 1988 On Liouville’s equation, accessory parameters, and the geometry of Teichmüller space for Riemann surfaces of genus 0. Zbl 0655.32022Zograf, P. G.; Takhtadzhyan, L. A. 22 1988 The Selberg zeta function and a new Kähler metric on the moduli space of punctured Riemann surfaces. Zbl 0739.30032Takhtadzhyan, L. A.; Zograf, P. G. 9 1988 Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman. Zbl 0632.58004Faddeev, L. D.; Takhtadzhyan, L. A. 67 1987 On uniformization of Riemann surfaces and the Weil-Petersson metric on Teichmüller and Schottky spaces. Zbl 0642.32011Zograf, P. G.; Takhtadzhyan, L. A. 11 1987 A local index theorem for families of \(\overline{\partial}\)-operators on Riemann surfaces. Zbl 0659.58043Zograf, P. G.; Takhtadzhyan, L. A. 10 1987 On Liouville equations, accessory parameters, and the geometry of Teichmüller spaces for Riemann surfaces of genus 0. Zbl 0642.32010Zograf, P. G.; Takhtadzhyan, L. A. 9 1987 A local index theorem for families of \({\bar \partial}\)-operators on Riemann surfaces. Zbl 0699.58061Zograf, P. G.; Takhtadzhyan, L. A. 8 1987 The zeta-function of the additive divisor problem and spectral decomposition of the automorphic Laplacian. Zbl 0609.10023Vinogradov, A. I.; Takhtadzhyan, L. A. 2 1987 Potential of the Weil-Petersson metric on the Torelli space. Zbl 0900.32007Zograf, P. G.; Takhtadzhyan, L. A. 1 1987 The potential of the Weil-Petersson metric on Torelli space. Zbl 0631.32020Zograf, P. G.; Takhtadzhyan, L. A. 1 1987 Hamiltonian methods in the theory of solitons. (Гамил’тонов подход в теории солитонов.) Zbl 0632.58003Takhtadzhyan, L. A.; Faddeev, L. D. 119 1986 Scattering theory for the Korteweg-de Vries (KdV) equation and its Hamiltonian interpretation. Zbl 0618.35100Buslaev, V. S.; Faddeev, L. D.; Takhtadzhan, L. A. 11 1986 Poisson structure for the KdV equation. Zbl 0595.35093Faddeev, L. D.; Takhtadzhan, L. A. 9 1985 Action of the Liouville equation is a generating function for the accessory parameters and the potential of the Weil-Petersson metric on the Teichmüller space. Zbl 0612.32018Zograf, P. G.; Takhtadzhyan, L. A. 5 1985 Simple connection between the geometric and the Hamiltonian representations of integrable nonlinear equations. Zbl 0562.35088Takhtadzhyan, L. A.; Faddeev, L. D. 2 1985 Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model. Zbl 0532.47009Faddeev, L. D.; Takhtadzhyan, L. A. 55 1984 The zeta-function of the additive divisor problem and the spectral expansion of the automorphic Laplacian. Zbl 0536.10025Vinogradov, A. I.; Takhtadzhyan, L. A. 12 1984 Analogues of the Gauss-Vinogradov formula on the critical line. Zbl 0534.10039Vinogradov, A. I.; Takhtadzhyan, L. A. 4 1984 Solutions of the triangle equations with \({\mathbb{Z}}_ n\times {\mathbb{Z}}_ n\)-symmetry and matrix analogues of the Weierstrass zeta- and sigma- functions. Zbl 0542.15003Takhtadzhyan, L. A. 3 1984 Integrable models in classical and quantum field theory. Zbl 0569.47010Takhtajan, L. A. 2 1984 Analogues of the Vinogradov-Gauss formula in the critical strip. Zbl 0523.12011Vinogradov, A. I.; Takhtadzhyan, L. A. 1 1983 Theory of Eisenstein series for the group SL(3,R) and its application to a binary problem. Zbl 0476.10024Vinogradov, A. I.; Takhtadzhyan, L. A. 11 1982 The Gauss-Hasse hypothesis on real quadratic fields with class number one. Zbl 0497.12004Takhtadzhan, L. A.; Vinogradov, A. I. 2 1982 A simple connection between geometric and Hamiltonian representations of integrable nonlinear equations. Zbl 0505.35082Takhtadzhyan, L. A.; Faddeev, L. D. 1 1982 An estimate of the residue of Rankin L-series. Zbl 0516.10017Vinogradov, A. I.; Takhtadzhyan, L. A. 1 1982 The spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model. Zbl 0471.47009Takhtadzhyan, L. A.; Faddeev, L. D. 12 1981 Analogues of the Gauss-Vinogradov formula on the critical line. Zbl 0468.10023Takhtadzhyan, L. A.; Vinogradov, A. I. 5 1981 The quantum inverse problem method and the XYZ Heisenberg model. Zbl 1194.81247Takhtajan, Leon A. 3 1981 Analogs of the Vinogradov-Gauss formula in the critical strip. Zbl 0483.12002Vinogradov, A. I.; Takhtadzhyan, L. A. 2 1981 Quantum inverse problem method. I. Zbl 1138.37331Sklyanin, E. K.; Takhtadzhyan, L. A.; Faddeev, L. D. 164 1980 On the Linnik-Skubenko asymptotics. Zbl 0488.10017Vinogradov, A. I.; Takhtadzhyan, L. A. 6 1980 On analogues of the Vinogradov-Gauss formula. Zbl 0468.10022Vinogradov, A. I.; Takhtadzhyan, L. A. 5 1980 The quantum inverse problem method. I. Zbl 0449.35096Faddeev, L. D.; Sklyanin, E. K.; Takhtadzhyan, L. A. 19 1979 Asymptotic formula for the sum of the lengths of the periods of the quadratic irrationalities of discriminant D. Zbl 0442.10007Takhtadzhyan, L. A. 1 1979 Theory of Eisenstein series for the group \(\mathrm{SL}(3,\mathbb{R})\) and its application to a binary problem. I: Fourier expansion of the highest Eisenstein series. Zbl 0434.10020Vinogradov, A. I.; Takhtadzhyan, L. A. 11 1978 Hamiltonian systems connected with the Dirac equation. Zbl 0404.35087Tahtadzjan, L. A. 1 1977 The Hamiltonian system connected with the equation u//(xi,nu)+sin u=0. Zbl 0412.35065Takhtadzhyan, L. A.; Faddeev, L. D. 5 1976 Essentially nonlinear one-dimensional model of classical field theory. Zbl 0299.35063Tahtadzjan, L. A.; Faddeev, L. D. 30 1975 Complete description of solutions of the ’sine-Gordon’ equation. Zbl 0312.35051Zakharov, V. E.; Takhtadzhyan, L. A.; Faddeev, L. D. 24 1974 all cited Publications top 5 cited Publications all top 5 Cited by 1,890 Authors 26 Takhtajan, Leon Armenovich 24 Doikou, Anastasia 23 Slavnov, Nikita A. 21 Kulish, Petr Petrovich 19 Ragoucy, Eric 18 Guha, Partha 14 Bai, Ruipu 14 Mudrov, Andrey I. 13 Sakhnovich, Alexander L. 13 Shen, Yuliang 12 Ablowitz, Mark Jay 12 Teo, Lee-Peng 11 Gurevich, Dmitrii 11 Its, Alexander Rudolfovich 11 Pakuliak, Stanislav Z. 11 Talalov, Sergeĭ Vladimirovich 10 Belliard, Samuel 10 Derkachëv, Sergeĭ Èduardovich 10 Kozlowski, Karol Kajetan 10 Lukyanov, Sergei L. 10 Prykarpatsky, Anatoliy Karolevych 10 Van der Mee, Cornelis Victor Maria 9 Bazhanov, Vladimir V. 9 Demontis, Francesco 9 Niccoli, Giuliano 9 Schippers, Eric D. 9 Teschl, Gerald 8 Biondini, Gino 8 Biswas, Indranil 8 Casas Miras, José Manuel 8 Crampé, Nicolas 8 Gerdzhikov, Vladimir Stefanov 8 Jing, Naihuan 8 Maillet, Jean-Michel 8 Makhlouf, Abdenacer 8 Manojlović, Nenad 8 Mariño, Marcos 8 Reshetikhin, Nikolai Yu. 8 Saponov, Pavel A. 8 Tang, ShuAn 8 Vinogradov, Askol’d Ivanovich 7 Abramov, Viktor 7 Avan, Jean 7 Domrin, Andrei Victorovich 7 Eshaghi Gordji, Madjid 7 Faddeev, Lyudvig Dmitrievich 7 Galleas, Wellington 7 Grassi, Alba 7 Hayashi, Takahiro 7 Kirillov, Anatol N. 7 Landi, Giovanni 7 Lipovskij, V. D. 7 Park, Choonkil 7 Prinari, Barbara 7 Rubtsov, Vladimir Nikolaevich 7 Staubach, Wolfgang 7 Vakhnenko, Oleksiy O. 6 Bogolyubov, Nikolaĭ Mikhaĭlovich 6 Caudrelier, Vincent 6 Ding, Qing 6 Ercolani, Nicholas M. 6 Grahovski, Georgi G. 6 Hadasz, Leszek 6 Jaskólski, Zbigniew 6 Karakhanyan, David 6 Kirschner, Roland 6 Korepin, Vladimir E. 6 Ladra González, Manuel 6 Majid, Shahn 6 Menotti, Pietro 6 Molev, Alexander I. 6 Nepomechie, Rafael I. 6 Ortenzi, Giovanni 6 Park, Jinsung 6 Radnell, David 6 Sheng, Yunhe 6 Shepelsky, Dmitry 6 Silvestrov, Sergei D. 6 Zhang, Yaozhong 6 Zhang, Yufeng 6 Zhou, Ruguang 5 Bai, Chengming 5 Bikbaev, Ramil’ F. 5 Boutet de Monvel, Anne Marie 5 Brzeziński, Tomasz 5 Das, Apurba 5 Donin, Joseph 5 Foerster, Angela 5 Forest, M. Gregory 5 Frappat, Luc 5 Gao, Peng 5 Ghose Choudhury, Anindya 5 Göhmann, Frank 5 Gravejat, Philippe 5 Gutshabash, Evgenii Shimonovitch 5 Khabibullin, Ismagil Talgatovich 5 Hu, Naihong 5 Liu, Ming 5 Ma, Wen-Xiu 5 Manashov, Alexander N. ...and 1,790 more Authors all top 5 Cited in 256 Serials 131 Theoretical and Mathematical Physics 129 Communications in Mathematical Physics 129 Journal of Mathematical Physics 111 Nuclear Physics. B 78 Journal of Geometry and Physics 78 Journal of High Energy Physics 66 Letters in Mathematical Physics 60 Journal of Soviet Mathematics 45 Journal of Algebra 36 Journal of Mathematical Sciences (New York) 35 Physics Letters. A 28 Physica D 26 Journal of Nonlinear Mathematical Physics 24 Advances in Mathematics 21 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 20 Journal of Statistical Mechanics: Theory and Experiment 19 International Journal of Modern Physics A 19 Studies in Applied Mathematics 17 International Journal of Geometric Methods in Modern Physics 16 Journal of Physics A: Mathematical and Theoretical 15 Chaos, Solitons and Fractals 15 Duke Mathematical Journal 15 Transactions of the American Mathematical Society 14 Journal of Mathematical Analysis and Applications 13 Physics Letters. B 12 Journal of Pure and Applied Algebra 12 Annales Henri Poincaré 11 Reviews in Mathematical Physics 11 Acta Applicandae Mathematicae 10 Communications in Algebra 10 Ukrainian Mathematical Journal 10 Functional Analysis and its Applications 10 Mathematische Zeitschrift 9 Proceedings of the American Mathematical Society 9 Publications of the Research Institute for Mathematical Sciences, Kyoto University 8 International Journal of Modern Physics B 8 International Journal of Theoretical Physics 8 Israel Journal of Mathematics 8 Journal d’Analyse Mathématique 8 Annales de l’Institut Fourier 8 Journal of Differential Equations 8 Mathematische Annalen 8 Advances in Applied Clifford Algebras 8 Analysis and Mathematical Physics 7 Communications on Pure and Applied Mathematics 7 Reports on Mathematical Physics 7 Journal of Functional Analysis 7 Journal of Number Theory 7 Linear Algebra and its Applications 7 Proceedings of the Steklov Institute of Mathematics 7 Science China. Mathematics 6 Applied Mathematics and Computation 6 Inventiones Mathematicae 6 Annals of Global Analysis and Geometry 6 St. Petersburg Mathematical Journal 5 Modern Physics Letters A 5 Classical and Quantum Gravity 5 Mathematical Notes 5 Russian Mathematical Surveys 5 Compositio Mathematica 5 Geometriae Dedicata 5 Communications in Partial Differential Equations 5 Journal of Nonlinear Science 5 Nuclear Physics, B, Proceedings Supplements 5 Discrete and Continuous Dynamical Systems 5 Annales Academiae Scientiarum Fennicae. Mathematica 5 Mathematical Physics, Analysis and Geometry 5 Geometry & Topology 5 Journal of Algebra and its Applications 5 Frontiers of Mathematics in China 4 General Relativity and Gravitation 4 Journal of Statistical Physics 4 Linear and Multilinear Algebra 4 Integral Equations and Operator Theory 4 Applied Numerical Mathematics 4 Differential Geometry and its Applications 4 Annals of Physics 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 SIAM Journal on Mathematical Analysis 4 Selecta Mathematica. New Series 4 Journal of Inequalities and Applications 4 Algebras and Representation Theory 4 Journal of the European Mathematical Society (JEMS) 4 Acta Mathematica Sinica. English Series 4 Advances in High Energy Physics 4 Advances in Mathematical Physics 4 Journal of Geometric Mechanics 3 Applicable Analysis 3 Journal of Computational Physics 3 Lithuanian Mathematical Journal 3 Nonlinearity 3 Journal of Computational and Applied Mathematics 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Proceedings of the Japan Academy. Series A 3 Quaestiones Mathematicae 3 Ricerche di Matematica 3 Transactions of the Moscow Mathematical Society 3 Advances in Applied Mathematics 3 Applied Mathematics Letters 3 Science in China. Series A ...and 156 more Serials all top 5 Cited in 54 Fields 663 Quantum theory (81-XX) 463 Nonassociative rings and algebras (17-XX) 455 Partial differential equations (35-XX) 449 Dynamical systems and ergodic theory (37-XX) 230 Statistical mechanics, structure of matter (82-XX) 217 Associative rings and algebras (16-XX) 175 Differential geometry (53-XX) 146 Global analysis, analysis on manifolds (58-XX) 128 Functions of a complex variable (30-XX) 106 Several complex variables and analytic spaces (32-XX) 94 Algebraic geometry (14-XX) 89 Relativity and gravitational theory (83-XX) 82 Mechanics of particles and systems (70-XX) 79 Functional analysis (46-XX) 72 Ordinary differential equations (34-XX) 70 Number theory (11-XX) 64 Group theory and generalizations (20-XX) 48 Difference and functional equations (39-XX) 46 Operator theory (47-XX) 44 Topological groups, Lie groups (22-XX) 33 Special functions (33-XX) 24 Manifolds and cell complexes (57-XX) 22 Combinatorics (05-XX) 22 Numerical analysis (65-XX) 21 Linear and multilinear algebra; matrix theory (15-XX) 19 Category theory; homological algebra (18-XX) 17 Fluid mechanics (76-XX) 11 Algebraic topology (55-XX) 11 Optics, electromagnetic theory (78-XX) 10 Integral equations (45-XX) 10 Mechanics of deformable solids (74-XX) 9 \(K\)-theory (19-XX) 9 Probability theory and stochastic processes (60-XX) 8 Computer science (68-XX) 7 Commutative algebra (13-XX) 7 Approximations and expansions (41-XX) 6 Real functions (26-XX) 6 Biology and other natural sciences (92-XX) 5 History and biography (01-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Abstract harmonic analysis (43-XX) 4 Convex and discrete geometry (52-XX) 4 Statistics (62-XX) 4 Information and communication theory, circuits (94-XX) 3 General and overarching topics; collections (00-XX) 3 Measure and integration (28-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Mathematical logic and foundations (03-XX) 2 General algebraic systems (08-XX) 2 Potential theory (31-XX) 2 Integral transforms, operational calculus (44-XX) 2 Geometry (51-XX) 2 General topology (54-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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