Edit Profile (opens in new tab) Rapinchuk, Andrei S. Co-Author Distance Author ID: rapinchuk.andrei-s Published as: Rapinchuk, A. S.; Rapinchuk, Andrei S.; Rapinchuk, Andrei; Rapinchuk, A.; Rapincuk, A. S. more...less Documents Indexed: 96 Publications since 1978, including 3 Books 2 Further Contributions Co-Authors: 39 Co-Authors with 70 Joint Publications 1,460 Co-Co-Authors all top 5 Co-Authors 27 single-authored 17 Platonov, Vladimir Petrovich 17 Prasad, Gopal 14 Rapinchuk, Igor A. 10 Chernousov, Vladimir I. 5 Benyash-Krivets, Valeriĭ Vatslavovich 5 Bondarenko, Aleksandr Adamovich 4 Faddeev, Lyudvig Dmitrievich 4 Margulis, Grigoriĭ Aleksandrovich 4 Novikov, Sergeĭ Petrovich 4 Segev, Yoav 4 Zel’manov, Efim Isaakovich 3 Adyan, Sergeĭ Ivanovich 3 Potapchik, Alexander 2 Bukhshtaber, Viktor Matveevich 2 Corvaja, Pietro 2 Erovenko, Igor V. 2 Kozlov, Valeriĭ Vasil’evich 2 Parshin, Alexei N. 2 Ren, Jinbo 2 Rowen, Louis Halle 2 Yanchevskii, Vyacheslav Ivanovich 2 Zannier, Umberto M. 1 Barkovich, O. A. 1 Bux, Kai-Uwe 1 Demeio, Julian Lawrence 1 Efrat, Ido 1 Ershov, Mikhail V. 1 Funar, Louis 1 Garibaldi, Skip 1 Krashen, Daniel 1 Lifschitz, Lucy 1 Mal’tsev, Arkadiĭ Anatol’evich 1 Matzri, Eliyahu 1 Morgan, Aleksander 1 Osipov, Yuriĭ Sergeevich 1 Pierce, Richard Scott 1 Pollio, Timothy P. 1 Saltman, David J. 1 Seitz, Gary M. 1 Sury, Balasubramanian 1 Zalesski, Alexandre Efimovich 1 Zhizhchenko, Alexey B. all top 5 Serials 7 Doklady Akademii Nauk BSSR 7 Soviet Mathematics. Doklady 5 Russian Mathematical Surveys 4 Manuscripta Mathematica 4 Mathematics of the USSR. Izvestiya 4 Proceedings of the American Mathematical Society 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Journal of Number Theory 3 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 3 Proceedings of the Steklov Institute of Mathematics 2 Israel Journal of Mathematics 2 Publications Mathématiques 2 Inventiones Mathematicae 2 Journal of Algebra 2 IMRN. International Mathematics Research Notices 2 Mathematical Research Letters 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Algebra & Number Theory 1 Advances in Mathematics 1 Commentarii Mathematici Helvetici 1 Compositio Mathematica 1 Geometriae Dedicata 1 Journal of Soviet Mathematics 1 Mathematische Zeitschrift 1 Siberian Mathematical Journal 1 Transactions of the American Mathematical Society 1 Transactions of the Moscow Mathematical Society 1 Journal of the American Mathematical Society 1 Doklady Akademii Nauk Belarusi 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Notices of the American Mathematical Society 1 Russian Academy of Sciences. Izvestiya. Mathematics 1 Russian Academy of Sciences. Doklady. Mathematics 1 Geometry & Topology 1 Chebyshevskiĭ Sbornik 1 Cambridge Studies in Advanced Mathematics 1 Pure and Applied Mathematics (Academic Press) 1 Trudy Matematicheskogo Instituta Imeni V. A. Steklova 1 Translations. Series 2. American Mathematical Society 1 Groups, Geometry, and Dynamics 1 Bulletin of Mathematical Sciences 1 Research in the Mathematical Sciences all top 5 Fields 76 Group theory and generalizations (20-XX) 47 Number theory (11-XX) 24 Associative rings and algebras (16-XX) 18 Algebraic geometry (14-XX) 15 Topological groups, Lie groups (22-XX) 12 Field theory and polynomials (12-XX) 6 \(K\)-theory (19-XX) 5 History and biography (01-XX) 4 Combinatorics (05-XX) 4 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 75 Publications have been cited 972 times in 686 Documents Cited by ▼ Year ▼ Algebraic groups and number theory. Transl. from the Russian by Rachel Rowen. Zbl 0841.20046Platonov, Vladimir; Rapinchuk, Andrei 306 1994 Algebraic groups and number theory. Zbl 0806.11002Platonov, V. P.; Rapinchuk, A. S. 122 1992 Algebraic groups and number theory. (Алгебраические группы и теория чисел.) Zbl 0732.20027Platonov, V. P.; Rapinchuk, A. S. 58 1991 Weakly commensurable arithmetic groups and isospectral locally symmetric spaces. Zbl 1176.22011Prasad, Gopal; Rapinchuk, Andrei S. 39 2009 Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Zbl 1008.16018Rapinchuk, Andrei S.; Segev, Yoav; Seitz, Gary M. 28 2002 Computation of the metaplectic kernel. Zbl 0941.22019Prasad, Gopal; Rapinchuk, Andrei S. 28 1996 Representation varieties of the fundamental groups of compact orientable surfaces. Zbl 0857.14012Rapinchuk, A. S.; Benyash-Krivetz, V. V.; Chernousov, V. I. 23 1996 Existence of irreducible \(\mathbb R\)-regular elements in Zariski-dense subgroups. Zbl 1029.22020Prasad, Gopal; Rapinchuk, Andrei S. 22 2003 Local-global principles for embedding of fields with involution into simple algebras with involution. Zbl 1223.11047Prasad, Gopal; Rapinchuk, Andrei S. 15 2010 On the existence of isotropic forms of semi-simple algebraic groups over number fields with prescribed local behavior. Zbl 1132.20024Prasad, Gopal; Rapinchuk, Andrei S. 15 2006 Abstract properties of \(S\)-arithmetic groups and the congruence problem. Zbl 0785.20025Platonov, V. P.; Rapinchuk, A. S. 13 1992 Torus bundles not distinguished by TQFT invariants. With an appendix by Louis Funar and Andrei Rapinchuk. Zbl 1278.57020Funar, Louis 13 2013 Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces. Zbl 1347.20053Prasad, Gopal; Rapinchuk, Andrei S. 12 2014 Bounded generation of \(S\)-arithmetic subgroups of isotropic orthogonal groups over number fields. Zbl 1168.20020Erovenko, Igor V.; Rapinchuk, Andrei S. 12 2006 Strong approximation for algebraic groups. Zbl 1341.20042Rapinchuk, Andrei S. 11 2014 Valuation-like maps and the congruence subgroup property. Zbl 0999.16016Rapinchuk, Andrei S.; Segev, Yoav 11 2001 On division algebras having the same maximal subfields. Zbl 1205.16015Rapinchuk, Andrei S.; Rapinchuk, Igor A. 10 2010 Bounded generation of \(\mathrm{SL}_2\) over rings of \(S\)-integers with infinitely many units. Zbl 1448.11198Morgan, Aleksander; Rapinchuk, Andrei; Sury, Balasubramanian 10 2018 The congruence subgroup property for \(\operatorname{Aut} F_2\): a group-theoretic proof of Asada’s theorem. Zbl 1251.20035Bux, Kai-Uwe; Ershov, Mikhail V.; Rapinchuk, Andrei S. 10 2011 The genus of a division algebra and the unramified Brauer group. Zbl 1293.16015Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 10 2013 Spinor groups with good reduction. Zbl 1443.11031Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 10 2019 Division algebras with the same maximal subfields. Zbl 1325.12006Chernousov, V. I.; Rapinchuk, A. S.; Rapinchuk, I. A. 9 2015 On some finiteness properties of algebraic groups over finitely generated fields. (Sur quelques propriétés de finitude des groupes algébriques sur des corps de type fini.) Zbl 1376.14049Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 8 2016 Bounded generation of some \(S\)-arithmetic orthogonal groups. Zbl 1010.20033Erovenko, Igor V.; Rapinchuk, Andrei S. 8 2001 Zariski-dense subgroups and transcendental number theory. Zbl 1072.22009Prasad, Gopal; Rapinchuk, Andrei S. 8 2005 Irreducible tori in semisimple groups. Zbl 1057.22025Prasad, Gopal; Rapinchuk, Andrei S. 8 2001 On the size of the genus of a division algebra. Zbl 1356.16013Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 8 2016 Congruence subgroup problem for algebraic groups: Old and new. Zbl 0805.20040Rapinchuk, A. S. 8 1992 The congruence problem for arithmetic groups of finite width. Zbl 0745.20043Rapinchuk, A. S. 7 1990 On the group of rational points of three-dimensional groups. Zbl 0431.12012Platonov, V. P.; Rapinchuk, A. S. 7 1979 The finiteness of the genus of a finite-dimensional division algebra, and some generalizations. Zbl 1467.16018Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 7 2020 On the genus of a division algebra. Zbl 1272.16020Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 7 2012 Normal subgroups of \(SL_{1,D}\) and the classification of finite simple groups. Zbl 0879.20027Rapinchuk, Andrei; Potapchik, Alexander 6 1996 Low-dimensional linear representations of \(\operatorname{Aut} F_n\), \(n\geq 3\). Zbl 0942.20002Potapchik, A.; Rapinchuk, A. 6 2000 Weakly commensurable \(S\)-arithmetic subgroups in almost simple algebraic groups of types B and C. Zbl 1285.20045Garibaldi, Skip; Rapinchuk, Andrei 6 2013 On \(SS\)-rigid groups and A. Weil’s criterion for local rigidity. I. Zbl 0920.20004Rapinchuk, A. S. 6 1998 The multinorm principle for linearly disjoint Galois extensions. Zbl 1309.11078Pollio, Timothy P.; Rapinchuk, Andrei S. 6 2013 Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank \(> 1\) over Noetherian rings. Zbl 1232.19001Rapinchuk, Andrei S.; Rapinchuk, Igor A. 5 2011 On abstract homomorphisms of Chevalley groups with nonreductive image. I. Zbl 0987.20025Lifschitz, L.; Rapinchuk, A. 4 2001 Subnormal subgroups of the groups of rational points of reductive algebraic groups. Zbl 1007.20043Prasad, Gopal; Rapinchuk, Andrei S. 4 2002 Multiplicative arithmetic of division algebras over number fields, and the metaplectic problem. Zbl 0678.20031Rapinchuk, A. S. 4 1988 Multiplicative structure of skew fields over number fields and Hasse norm principle. Zbl 0559.12010Platonov, V. P.; Rapinchuk, A. S. 4 1984 The congruence subgroup problem for algebraic groups. Zbl 0725.20034Rapinchuk, A. 4 1990 The congruence subgroup problem. Zbl 1125.20313Rapinchuk, A. S. 4 1999 Generic elements of a Zariski-dense subgroup form an open subset. Zbl 1423.22015Prasad, G.; Rapinchuk, A. S. 4 2017 Non-virtually abelian anisotropic linear groups are not boundedly generated. Zbl 1491.11045Corvaja, Pietro; Rapinchuk, Andrei S.; Ren, Jinbo; Zannier, Umberto M. 4 2022 The multiplicative structure of division rings over number fields, and the Hasse principle. Zbl 0516.20029Platonov, V. P.; Rapinchuk, A. S. 3 1982 Class number of algebraic groups. Zbl 0425.20038Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 3 1979 The congruence problem for algebraic groups and strong approximations in affine varieties. Zbl 0661.20034Rapinchuk, A. S. 3 1988 On the fields generated by the lengths of closed geodesics in locally symmetric spaces. Zbl 1308.53077Prasad, Gopal; Rapinchuk, Andrei S. 3 2014 On the congruence kernel for simple algebraic groups. Zbl 1356.20031Prasad, Gopal; Rapinchuk, Andrei S. 3 2016 On the congruence problem for algebraic groups. Zbl 0692.20033Rapinchuk, A. S. 3 1989 The Margulis-Platonov conjecture for \(\text{SL}_{1,D}\) and 2-generation of finite simple groups. Zbl 1101.20027Rapinchuk, Andrei S. 3 2006 The geometric theory of representations for the fundamental groups of compact oriented surfaces. Zbl 0840.20031Rapinchuk, A. S.; Benyash-Krivets, V. V. 3 1993 On the finite dimensional unitary representations of Kazhdan groups. Zbl 0926.22001Rapinchuk, A. 3 1999 Towards the eigenvalue rigidity of Zariski-dense subgroups. Zbl 1373.20063Rapinchuk, Andrei S. 3 2014 Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields. Zbl 1489.11059Rapinchuk, Andrei S.; Rapinchuk, Igor A. 3 2022 Associative algebras. (Assotsiativnye algebry). Transl. from the English by A. S. Rapinchuk and V. I. Yanchevskij. Transl. ed. and with a preface by A. E. Zalesskij. Zbl 0671.16001Pierce, Richard S. 2 1986 The Hasse principle for symmetric spaces. Zbl 0679.14027Rapinchuk, A. S. 2 1987 Algebraic groups. Zbl 0564.20023Platonov, V. P.; Rapinchuk, A. S. 2 1983 Platonov’s conjecture on the genus in arithmetic groups. Zbl 0477.20027Rapinchuk, A. S. 2 1981 Number-theoretic techniques in the theory of Lie groups and differential geometry. Zbl 1209.22006Prasad, Gopal; Rapinchuk, Andrei S. 2 2010 Linear algebraic groups with good reduction. Zbl 1466.20032Rapinchuk, Andrei S.; Rapinchuk, Igor A. 2 2020 Representations of groups of finite width. Zbl 0777.20014Rapinchuk, A. S. 1 1990 On the estimation of the number of double classes of adele groups of algebraic groups. Zbl 0393.20031Bondarenko, A. A.; Rapincuk, A. S. 1 1978 Erratum: Irreducible tori in semisimple groups. Zbl 1099.22501Prasad, Gopal; Rapinchuk, Andrei S. 1 2002 \(n\)-dimensional linear representations of \(\operatorname{Aut} F_ n\), and more. Zbl 0891.20024Rapinchuk, Andrei S. 1 1997 Nonabelian free subgroups in homomorphic images of valued quaternion division algebras. Zbl 1117.16007Rapinchuk, Andrei S.; Rowen, Louis; Segev, Yoav 1 2006 Class numbers and groups of algebraic groups. Zbl 0448.20045Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1980 Klassenzahlen und Klassengruppen algebraischer Gruppen. II. Zbl 0453.20033Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1980 Class numbers and groups of algebraic groups. II. Zbl 0464.20031Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1981 Class numbers in the genus of quadratic forms and algebraic groups. Zbl 0473.20032Rapinchuk, A. S. 1 1981 Multiplicative arithmetic of division algebras over number fields and the metaplectic problem. Zbl 0631.20034Rapinchuk, A. S. 1 1987 Finiteness theorems for algebraic tori over function fields. Zbl 1473.14093Rapinchuk, Andrei S.; Rapinchuk, Igor A. 1 2021 Bounded generation by semi-simple elements: quantitative results. (Engendrement borné par éléments semi-simples: résultats quantitatifs.) Zbl 07630945Corvaja, Pietro; Demeio, Julian L.; Rapinchuk, Andrei S.; Ren, Jinbo; Zannier, Umberto M. 1 2022 Non-virtually abelian anisotropic linear groups are not boundedly generated. Zbl 1491.11045Corvaja, Pietro; Rapinchuk, Andrei S.; Ren, Jinbo; Zannier, Umberto M. 4 2022 Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields. Zbl 1489.11059Rapinchuk, Andrei S.; Rapinchuk, Igor A. 3 2022 Bounded generation by semi-simple elements: quantitative results. (Engendrement borné par éléments semi-simples: résultats quantitatifs.) Zbl 07630945Corvaja, Pietro; Demeio, Julian L.; Rapinchuk, Andrei S.; Ren, Jinbo; Zannier, Umberto M. 1 2022 Finiteness theorems for algebraic tori over function fields. Zbl 1473.14093Rapinchuk, Andrei S.; Rapinchuk, Igor A. 1 2021 The finiteness of the genus of a finite-dimensional division algebra, and some generalizations. Zbl 1467.16018Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 7 2020 Linear algebraic groups with good reduction. Zbl 1466.20032Rapinchuk, Andrei S.; Rapinchuk, Igor A. 2 2020 Spinor groups with good reduction. Zbl 1443.11031Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 10 2019 Bounded generation of \(\mathrm{SL}_2\) over rings of \(S\)-integers with infinitely many units. Zbl 1448.11198Morgan, Aleksander; Rapinchuk, Andrei; Sury, Balasubramanian 10 2018 Generic elements of a Zariski-dense subgroup form an open subset. Zbl 1423.22015Prasad, G.; Rapinchuk, A. S. 4 2017 On some finiteness properties of algebraic groups over finitely generated fields. (Sur quelques propriétés de finitude des groupes algébriques sur des corps de type fini.) Zbl 1376.14049Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 8 2016 On the size of the genus of a division algebra. Zbl 1356.16013Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 8 2016 On the congruence kernel for simple algebraic groups. Zbl 1356.20031Prasad, Gopal; Rapinchuk, Andrei S. 3 2016 Division algebras with the same maximal subfields. Zbl 1325.12006Chernousov, V. I.; Rapinchuk, A. S.; Rapinchuk, I. A. 9 2015 Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces. Zbl 1347.20053Prasad, Gopal; Rapinchuk, Andrei S. 12 2014 Strong approximation for algebraic groups. Zbl 1341.20042Rapinchuk, Andrei S. 11 2014 On the fields generated by the lengths of closed geodesics in locally symmetric spaces. Zbl 1308.53077Prasad, Gopal; Rapinchuk, Andrei S. 3 2014 Towards the eigenvalue rigidity of Zariski-dense subgroups. Zbl 1373.20063Rapinchuk, Andrei S. 3 2014 Torus bundles not distinguished by TQFT invariants. With an appendix by Louis Funar and Andrei Rapinchuk. Zbl 1278.57020Funar, Louis 13 2013 The genus of a division algebra and the unramified Brauer group. Zbl 1293.16015Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 10 2013 Weakly commensurable \(S\)-arithmetic subgroups in almost simple algebraic groups of types B and C. Zbl 1285.20045Garibaldi, Skip; Rapinchuk, Andrei 6 2013 The multinorm principle for linearly disjoint Galois extensions. Zbl 1309.11078Pollio, Timothy P.; Rapinchuk, Andrei S. 6 2013 On the genus of a division algebra. Zbl 1272.16020Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 7 2012 The congruence subgroup property for \(\operatorname{Aut} F_2\): a group-theoretic proof of Asada’s theorem. Zbl 1251.20035Bux, Kai-Uwe; Ershov, Mikhail V.; Rapinchuk, Andrei S. 10 2011 Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank \(> 1\) over Noetherian rings. Zbl 1232.19001Rapinchuk, Andrei S.; Rapinchuk, Igor A. 5 2011 Local-global principles for embedding of fields with involution into simple algebras with involution. Zbl 1223.11047Prasad, Gopal; Rapinchuk, Andrei S. 15 2010 On division algebras having the same maximal subfields. Zbl 1205.16015Rapinchuk, Andrei S.; Rapinchuk, Igor A. 10 2010 Number-theoretic techniques in the theory of Lie groups and differential geometry. Zbl 1209.22006Prasad, Gopal; Rapinchuk, Andrei S. 2 2010 Weakly commensurable arithmetic groups and isospectral locally symmetric spaces. Zbl 1176.22011Prasad, Gopal; Rapinchuk, Andrei S. 39 2009 On the existence of isotropic forms of semi-simple algebraic groups over number fields with prescribed local behavior. Zbl 1132.20024Prasad, Gopal; Rapinchuk, Andrei S. 15 2006 Bounded generation of \(S\)-arithmetic subgroups of isotropic orthogonal groups over number fields. Zbl 1168.20020Erovenko, Igor V.; Rapinchuk, Andrei S. 12 2006 The Margulis-Platonov conjecture for \(\text{SL}_{1,D}\) and 2-generation of finite simple groups. Zbl 1101.20027Rapinchuk, Andrei S. 3 2006 Nonabelian free subgroups in homomorphic images of valued quaternion division algebras. Zbl 1117.16007Rapinchuk, Andrei S.; Rowen, Louis; Segev, Yoav 1 2006 Zariski-dense subgroups and transcendental number theory. Zbl 1072.22009Prasad, Gopal; Rapinchuk, Andrei S. 8 2005 Existence of irreducible \(\mathbb R\)-regular elements in Zariski-dense subgroups. Zbl 1029.22020Prasad, Gopal; Rapinchuk, Andrei S. 22 2003 Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Zbl 1008.16018Rapinchuk, Andrei S.; Segev, Yoav; Seitz, Gary M. 28 2002 Subnormal subgroups of the groups of rational points of reductive algebraic groups. Zbl 1007.20043Prasad, Gopal; Rapinchuk, Andrei S. 4 2002 Erratum: Irreducible tori in semisimple groups. Zbl 1099.22501Prasad, Gopal; Rapinchuk, Andrei S. 1 2002 Valuation-like maps and the congruence subgroup property. Zbl 0999.16016Rapinchuk, Andrei S.; Segev, Yoav 11 2001 Bounded generation of some \(S\)-arithmetic orthogonal groups. Zbl 1010.20033Erovenko, Igor V.; Rapinchuk, Andrei S. 8 2001 Irreducible tori in semisimple groups. Zbl 1057.22025Prasad, Gopal; Rapinchuk, Andrei S. 8 2001 On abstract homomorphisms of Chevalley groups with nonreductive image. I. Zbl 0987.20025Lifschitz, L.; Rapinchuk, A. 4 2001 Low-dimensional linear representations of \(\operatorname{Aut} F_n\), \(n\geq 3\). Zbl 0942.20002Potapchik, A.; Rapinchuk, A. 6 2000 The congruence subgroup problem. Zbl 1125.20313Rapinchuk, A. S. 4 1999 On the finite dimensional unitary representations of Kazhdan groups. Zbl 0926.22001Rapinchuk, A. 3 1999 On \(SS\)-rigid groups and A. Weil’s criterion for local rigidity. I. Zbl 0920.20004Rapinchuk, A. S. 6 1998 \(n\)-dimensional linear representations of \(\operatorname{Aut} F_ n\), and more. Zbl 0891.20024Rapinchuk, Andrei S. 1 1997 Computation of the metaplectic kernel. Zbl 0941.22019Prasad, Gopal; Rapinchuk, Andrei S. 28 1996 Representation varieties of the fundamental groups of compact orientable surfaces. Zbl 0857.14012Rapinchuk, A. S.; Benyash-Krivetz, V. V.; Chernousov, V. I. 23 1996 Normal subgroups of \(SL_{1,D}\) and the classification of finite simple groups. Zbl 0879.20027Rapinchuk, Andrei; Potapchik, Alexander 6 1996 Algebraic groups and number theory. Transl. from the Russian by Rachel Rowen. Zbl 0841.20046Platonov, Vladimir; Rapinchuk, Andrei 306 1994 The geometric theory of representations for the fundamental groups of compact oriented surfaces. Zbl 0840.20031Rapinchuk, A. S.; Benyash-Krivets, V. V. 3 1993 Algebraic groups and number theory. Zbl 0806.11002Platonov, V. P.; Rapinchuk, A. S. 122 1992 Abstract properties of \(S\)-arithmetic groups and the congruence problem. Zbl 0785.20025Platonov, V. P.; Rapinchuk, A. S. 13 1992 Congruence subgroup problem for algebraic groups: Old and new. Zbl 0805.20040Rapinchuk, A. S. 8 1992 Algebraic groups and number theory. (Алгебраические группы и теория чисел.) Zbl 0732.20027Platonov, V. P.; Rapinchuk, A. S. 58 1991 The congruence problem for arithmetic groups of finite width. Zbl 0745.20043Rapinchuk, A. S. 7 1990 The congruence subgroup problem for algebraic groups. Zbl 0725.20034Rapinchuk, A. 4 1990 Representations of groups of finite width. Zbl 0777.20014Rapinchuk, A. S. 1 1990 On the congruence problem for algebraic groups. Zbl 0692.20033Rapinchuk, A. S. 3 1989 Multiplicative arithmetic of division algebras over number fields, and the metaplectic problem. Zbl 0678.20031Rapinchuk, A. S. 4 1988 The congruence problem for algebraic groups and strong approximations in affine varieties. Zbl 0661.20034Rapinchuk, A. S. 3 1988 The Hasse principle for symmetric spaces. Zbl 0679.14027Rapinchuk, A. S. 2 1987 Multiplicative arithmetic of division algebras over number fields and the metaplectic problem. Zbl 0631.20034Rapinchuk, A. S. 1 1987 Associative algebras. (Assotsiativnye algebry). Transl. from the English by A. S. Rapinchuk and V. I. Yanchevskij. Transl. ed. and with a preface by A. E. Zalesskij. Zbl 0671.16001Pierce, Richard S. 2 1986 Multiplicative structure of skew fields over number fields and Hasse norm principle. Zbl 0559.12010Platonov, V. P.; Rapinchuk, A. S. 4 1984 Algebraic groups. Zbl 0564.20023Platonov, V. P.; Rapinchuk, A. S. 2 1983 The multiplicative structure of division rings over number fields, and the Hasse principle. Zbl 0516.20029Platonov, V. P.; Rapinchuk, A. S. 3 1982 Platonov’s conjecture on the genus in arithmetic groups. Zbl 0477.20027Rapinchuk, A. S. 2 1981 Class numbers and groups of algebraic groups. II. Zbl 0464.20031Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1981 Class numbers in the genus of quadratic forms and algebraic groups. Zbl 0473.20032Rapinchuk, A. S. 1 1981 Class numbers and groups of algebraic groups. Zbl 0448.20045Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1980 Klassenzahlen und Klassengruppen algebraischer Gruppen. II. Zbl 0453.20033Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1980 On the group of rational points of three-dimensional groups. Zbl 0431.12012Platonov, V. P.; Rapinchuk, A. S. 7 1979 Class number of algebraic groups. Zbl 0425.20038Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 3 1979 On the estimation of the number of double classes of adele groups of algebraic groups. Zbl 0393.20031Bondarenko, A. A.; Rapincuk, A. S. 1 1978 all cited Publications top 5 cited Publications all top 5 Cited by 705 Authors 35 Rapinchuk, Andrei S. 20 Lubotzky, Alexander 15 Nguyễn Quôc Thăng 15 Rapinchuk, Igor A. 14 Chernousov, Vladimir I. 10 Prasad, Gopal 9 Parimala, Raman 8 Einsiedler, Manfred Leopold 8 Linowitz, Benjamin 8 McReynolds, David Ben 8 Oh, Hee 7 Avni, Nir 7 Garibaldi, Skip 7 Margulis, Grigoriĭ Aleksandrovich 6 Belolipetsky, Mikhail V. 6 Gelander, Tsachik 6 Gille, Philippe 6 Gorodnik, Alexander 6 Grunewald, Fritz J. 6 Kaletha, Tasho 6 Mohammadi, Amir 6 Segev, Yoav 6 Vavilov, Nikolaĭ Aleksandrovich 6 Venkataramana, Tyakal Nanjundiah 6 Wei, Dasheng 6 Witte Morris, Dave 6 Xu, Fei 5 Aka, Menny 5 Bayer-Fluckiger, Eva 5 Ben-Ezra, David El-Chai 5 Benyash-Krivets, Valeriĭ Vatslavovich 5 Gordeev, Nikolai L. 5 Kammeyer, Holger 5 Kunyavskiĭ, Boris Èmmanuilovich 5 Larsen, Michael Jeffrey 5 Sarnak, Peter Clive 5 Stover, Matthew 5 Sury, Balasubramanian 5 Yafaev, Andrei 5 Yu, Chia-Fu 4 Arenas-Carmona, Luis 4 Bitan, Rony A. 4 Borovoi, Mikhail V. 4 Cao, Yang 4 Chan, Wai Kiu 4 Choiy, Kwangho 4 Colliot-Thélène, Jean-Louis 4 Emery, Vincent 4 Fiori, Andrew 4 Liebeck, Martin Walter 4 Meyer, Jeffrey S. 4 Platonov, Vladimir Petrovich 4 Rowen, Louis Halle 4 Shapira, Uri 4 Thakur, Maneesh L. 4 Ullmo, Emmanuel 4 Venkatesh, Akshay 4 Vishne, Uzi 4 Wortman, Kevin A. 4 Zalesskii, Pavel 3 Benoist, Yves 3 Bou-Rabee, Khalid 3 Breuillard, Emmanuel 3 Bridson, Martin R. 3 Bundy, David M. 3 del Río, Angel 3 Flicker, Yuval Z. 3 Gao, Ziyang 3 Glasner, Yair 3 Gross, Benedict Hyman 3 Hooda, Neha 3 Jaikin-Zapirain, Andrei 3 Kim, Henry H. 3 Kim, Inkang 3 Klopsch, Benjamin 3 Köhl, Ralf 3 Krashen, Daniel 3 Lee, Ting-Yu 3 Levit, Arie 3 Lim, Seonhee 3 Lindenstrauss, Elon 3 Loughran, Daniel 3 Luethi, Manuel 3 Mahdavi-Hezavehi, M. 3 Martin, Benjamin M. S. 3 Mazur, Marcin 3 Mila, Olivier 3 Ngô Thi Ngoan 3 Onn, Uri 3 Pillay, Anand 3 Reid, Alan W. 3 Rowley, Peter J. 3 Rühr, Rene 3 Samuels, Beth 3 Sauer, Roman 3 Segal, Daniel 3 Shalev, Aner 3 Sikora, Adam S. 3 Soifer, Grigoriĭ Aleksandrovich 3 Sorensen, Claus Mazanti ...and 605 more Authors all top 5 Cited in 141 Serials 51 Journal of Algebra 30 Israel Journal of Mathematics 29 Duke Mathematical Journal 28 Transactions of the American Mathematical Society 24 Journal of Number Theory 24 Proceedings of the American Mathematical Society 23 Mathematische Zeitschrift 20 Inventiones Mathematicae 18 Advances in Mathematics 15 Geometriae Dedicata 13 Compositio Mathematica 13 Annals of Mathematics. Second Series 12 Michigan Mathematical Journal 11 Journal of Pure and Applied Algebra 11 Journal of Mathematical Sciences (New York) 11 Forum of Mathematics, Sigma 10 Communications in Algebra 10 Mathematische Annalen 10 Journal of the American Mathematical Society 10 Geometric and Functional Analysis. GAFA 8 Annales de l’Institut Fourier 8 Publications Mathématiques 8 Journal für die Reine und Angewandte Mathematik 8 Manuscripta Mathematica 8 Journal of the European Mathematical Society (JEMS) 8 Proceedings of the Steklov Institute of Mathematics 8 Algebra & Number Theory 7 Memoirs of the American Mathematical Society 6 Journal of the London Mathematical Society. Second Series 6 Ergodic Theory and Dynamical Systems 6 International Journal of Algebra and Computation 6 Geometry & Topology 6 Algebraic & Geometric Topology 6 International Journal of Number Theory 5 Documenta Mathematica 5 Representation Theory 5 Journal of Group Theory 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Journal of Algebra and its Applications 5 Journal of Modern Dynamics 4 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 4 Nagoya Mathematical Journal 4 Pacific Journal of Mathematics 4 Journal of the Institute of Mathematics of Jussieu 3 Journal d’Analyse Mathématique 3 Mathematical Notes 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Archiv der Mathematik 3 Bulletin of the London Mathematical Society 3 Journal of the Mathematical Society of Japan 3 Journal of Soviet Mathematics 3 Mathematika 3 Proceedings of the Japan Academy. Series A 3 Proceedings of the London Mathematical Society. Third Series 3 Siberian Mathematical Journal 3 Annals of Pure and Applied Logic 3 Forum Mathematicum 3 Bulletin of the American Mathematical Society. New Series 3 Transformation Groups 3 Doklady Mathematics 3 Groups, Geometry, and Dynamics 3 European Journal of Mathematics 2 Communications in Mathematical Physics 2 Linear and Multilinear Algebra 2 Mathematics of Computation 2 Acta Arithmetica 2 Commentarii Mathematici Helvetici 2 Functiones et Approximatio. Commentarii Mathematici 2 Journal of Functional Analysis 2 Monatshefte für Mathematik 2 European Journal of Combinatorics 2 International Journal of Mathematics 2 IMRN. International Mathematics Research Notices 2 Linear Algebra and its Applications 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Journal de Théorie des Nombres de Bordeaux 2 Bulletin des Sciences Mathématiques 2 Trudy Instituta Matematiki 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Journal of Noncommutative Geometry 2 Research in Number Theory 1 Bulletin of the Australian Mathematical Society 1 Communications on Pure and Applied Mathematics 1 Russian Mathematical Surveys 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Mathematica 1 Algebra and Logic 1 Bulletin de la Société Mathématique de France 1 Canadian Mathematical Bulletin 1 Journal of Combinatorial Theory. Series A 1 Journal of Geometry 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Transactions of the Moscow Mathematical Society 1 Topology and its Applications 1 Bulletin of the Korean Mathematical Society 1 Combinatorica 1 Annals of Global Analysis and Geometry 1 Bulletin of the Iranian Mathematical Society 1 Graphs and Combinatorics ...and 41 more Serials all top 5 Cited in 40 Fields 352 Number theory (11-XX) 344 Group theory and generalizations (20-XX) 191 Topological groups, Lie groups (22-XX) 164 Algebraic geometry (14-XX) 57 Dynamical systems and ergodic theory (37-XX) 50 Associative rings and algebras (16-XX) 45 Manifolds and cell complexes (57-XX) 37 Field theory and polynomials (12-XX) 37 Differential geometry (53-XX) 29 Combinatorics (05-XX) 25 Nonassociative rings and algebras (17-XX) 19 \(K\)-theory (19-XX) 17 Global analysis, analysis on manifolds (58-XX) 16 Geometry (51-XX) 13 Several complex variables and analytic spaces (32-XX) 12 Mathematical logic and foundations (03-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 9 Category theory; homological algebra (18-XX) 8 Functional analysis (46-XX) 7 Functions of a complex variable (30-XX) 7 Algebraic topology (55-XX) 6 Commutative algebra (13-XX) 6 Measure and integration (28-XX) 5 Abstract harmonic analysis (43-XX) 5 Probability theory and stochastic processes (60-XX) 3 Convex and discrete geometry (52-XX) 3 General topology (54-XX) 3 Quantum theory (81-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Computer science (68-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Relativity and gravitational theory (83-XX) 1 Biology and other natural sciences (92-XX) Citations by Year