Edit Profile (opens in new tab) Sarnak, Peter Clive Co-Author Distance Author ID: sarnak.peter-c Published as: Sarnak, Peter; Sarnak, P.; Sarnak, Peter C. more...less Further Spellings: Sarnak Peter C Homepage: https://www.math.princeton.edu/people/peter-sarnak External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef · theses.fr Videos: carmin.tv Awards: Wolf Prize (2014) · Shaw Prize (2024) Documents Indexed: 160 Publications since 1980, including 4 Books and 3 Additional arXiv Preprints 13 Contributions as Editor · 6 Further Contributions Biographic References: 3 Publications Co-Authors: 108 Co-Authors with 118 Joint Publications 3,425 Co-Co-Authors all top 5 Co-Authors 55 single-authored 17 Phillips, Ralph Saul 13 Rudnick, Zeév 9 Bourgain, Jean 8 Luo, Wenzhi 6 Gamburd, Alexander 6 Iwaniec, Henryk 5 Ghosh, Amit 4 Gelbart, Stephen S. 4 Osgood, Brad G. 3 Cogdell, James W. 3 Hejhal, Dennis A. 3 Howe, Roger Evans 3 Kontorovich, Alex V. 3 Lax, Peter David 3 Li, Jian-Shu 3 Lindenstrauss, Elon 3 Liu, Jianya 3 Lubotzky, Alexander 3 Majda, Andrew J. 3 Piatetski-Shapiro, Ilya 3 Wigman, Igor 2 Burger, Marc 2 Canzani, Yaiza 2 Eskin, Alex 2 Gindikin, Simon Grigorevich 2 Hafner, James Lee 2 Jakobson, Dmitry 2 Katz, Nicholas Michael 2 Kollár, Alicia J. 2 Kuhn, Harold William 2 Meiri, Chen 2 Nirenberg, Louis 2 Reznikov, Andre 2 Shahidi, Freydoon 2 Weisfeld, Morris 2 Zaharescu, Alexandru 1 Adams, Scot 1 Adem, Alejandro 1 Alexanderson, Gerald L. 1 Aravinda, C. S. 1 Barcelo, Hélène 1 Beheshti, Roya 1 Blasius, Don 1 Böcherer, Siegfried 1 Buser, Peter 1 Clozel, Laurent 1 Cohen, Charles J. 1 Conway, John Horton 1 Coskun, Izzet 1 Daubechies, Ingrid 1 Davidoff, Giuliana 1 Delbaen, Freddy 1 DeMarco, Laura Grace 1 Deshouillers, Jean-Marc 1 Detinko, Alla S. 1 Diamond, Harold George 1 Drinfeld, Vladimir Gershonovich 1 Driver, Kathy A. 1 Duke, William Drexel 1 Dumas, David 1 Efrat, Isaac Y. 1 Eisenbud, David 1 Epstein, Charles Lawrence 1 Fitzpatrick, Mattias 1 Fuchs, Elena D. 1 Goldfeld, Dorian Morris 1 Grigor’yan, Alexander Asaturovich 1 Guth, Lawrence David 1 Hales, Thomas Callister 1 Hamenstädt, Ursula 1 Houck, Andrew A. 1 Il’yashenko, Yuliĭ Sergeevich 1 Jacquet, Hervé Michel 1 Jitomirskaya, Svetlana Yakovlevna 1 Kapovich, Michael 1 Katok, Svetlana R. 1 Kelmer, Dubi 1 Kenig, Carlos Eduardo 1 Kennedy, Stephen Francis 1 Kim, Henry H. 1 Klainerman, Sergiu 1 Kolountzakis, Mihail N. 1 Kuksin, Sergeĭ B. 1 Lapid, Erez Moshe 1 Lubinsky, Doron S. 1 Macintyre, Angus John 1 Margulis, Grigoriĭ Aleksandrovich 1 McCurley, Kevin S. 1 Milman, Vitali D. 1 Mostow, George Daniel 1 Nestordi, Evita 1 Nevo, Amos 1 Osserman, Robert 1 Parzanchevski, Ori 1 Petridis, Yiannis N. 1 Pisier, Gilles 1 Pollatsek, Harriet S. 1 Quine, John R. 1 Ramakrishnan, Dinakar 1 Rassias, Michael Th. ...and 35 more Co-Authors all top 5 Serials 10 Duke Mathematical Journal 9 Inventiones Mathematicae 9 Notices of the American Mathematical Society 8 Communications on Pure and Applied Mathematics 7 Communications in Mathematical Physics 7 Bulletin of the American Mathematical Society. New Series 5 Acta Mathematica 5 Journal of Functional Analysis 5 Geometric and Functional Analysis. GAFA 4 Israel Journal of Mathematics 4 Journal of Number Theory 4 Journal of the European Mathematical Society (JEMS) 3 Journal of the American Mathematical Society 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Contemporary Mathematics 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Publications Mathématiques 2 Combinatorica 2 IMRN. International Mathematics Research Notices 2 Proceedings of the National Academy of Sciences of the United States of America 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Annals of Mathematics. Second Series 2 Cambridge Tracts in Mathematics 2 Israel Mathematical Conference Proceedings 2 Springer Collected Works in Mathematics 1 American Mathematical Monthly 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Acta Arithmetica 1 Advances in Mathematics 1 American Journal of Mathematics 1 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 1 Mathematische Zeitschrift 1 Transactions of the American Mathematical Society 1 Ergodic Theory and Dynamical Systems 1 Bulletin of the Iranian Mathematical Society 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Indagationes Mathematicae. New Series 1 New Zealand Journal of Mathematics 1 Experimental Mathematics 1 Documenta Mathematica 1 European Mathematical Society Newsletter 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 Journal of Evolution Equations 1 Moscow Mathematical Journal 1 Milan Journal of Mathematics 1 Colloquium Publications. American Mathematical Society 1 London Mathematical Society Student Texts 1 IAS/Park City Mathematics Series 1 Communications in Mathematical Analysis 1 Journal of Modern Dynamics 1 Mathematics Newsletter 1 Notices of the South African Mathematical Society 1 Communications of the American Mathematical Society all top 5 Fields 128 Number theory (11-XX) 25 Global analysis, analysis on manifolds (58-XX) 23 Topological groups, Lie groups (22-XX) 19 History and biography (01-XX) 19 Dynamical systems and ergodic theory (37-XX) 17 Partial differential equations (35-XX) 13 Functions of a complex variable (30-XX) 13 Differential geometry (53-XX) 13 Quantum theory (81-XX) 12 Algebraic geometry (14-XX) 9 General and overarching topics; collections (00-XX) 9 Combinatorics (05-XX) 8 Probability theory and stochastic processes (60-XX) 7 Group theory and generalizations (20-XX) 6 Operator theory (47-XX) 5 Measure and integration (28-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Abstract harmonic analysis (43-XX) 4 Functional analysis (46-XX) 3 Convex and discrete geometry (52-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Special functions (33-XX) 2 General topology (54-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Real functions (26-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 147 Publications have been cited 6,039 times in 3,797 Documents Cited by ▼ Year ▼ Ramanujan graphs. Zbl 0661.05035 Lubotzky, A.; Phillips, R.; Sarnak, P. 533 1988 Functoriality for the exterior square of \(\text{GL}_4\) and the symmetric fourth of \(\text{GL}_2\). Appendix 1 by Dinakar Ramakrishnan, Appendix 2 by Henry H. Kim and Peter Sarnak. Zbl 1018.11024 Kim, Henry H. 438 2003 Random matrices, Frobenius eigenvalues, and monodromy. Zbl 0958.11004 Katz, Nicholas M.; Sarnak, Peter 289 1999 Zeros of principal \(L\)-functions and random matrix theory. Zbl 0866.11050 Rudnick, Zeév; Sarnak, Peter 231 1996 Extremals of determinants of Laplacians. Zbl 0653.53022 Osgood, B.; Phillips, R.; Sarnak, P. 220 1988 Low lying zeros of families of \(L\)-functions. Zbl 1012.11041 Iwaniec, Henryk; Luo, Wenzhi; Sarnak, Peter 200 2000 Zeroes of zeta functions and symmetry. Zbl 0921.11047 Katz, Nicholas M.; Sarnak, Peter 177 1999 Density of integer points on affine homogeneous varieties. Zbl 0798.11024 Duke, W.; Rudnick, Z.; Sarnak, P. 138 1993 The behaviour of eigenstates of arithmetic hyperbolic manifolds. Zbl 0836.58043 Rudnick, Zeév; Sarnak, Peter 134 1994 Elementary number theory, group theory and Ramanujan graphs. Zbl 1032.11001 Davidoff, Giuliana; Sarnak, Peter; Valette, Alain 122 2003 Determinants of Laplacians. Zbl 0618.10023 Sarnak, Peter 107 1987 Some applications of modular forms. Zbl 0721.11015 Sarnak, Peter 103 1990 On Selberg’s eigenvalue conjecture. Zbl 0844.11038 Luo, W.; Rudnick, Z.; Sarnak, P. 100 1995 On the generalized Ramanujan conjecture for \(\text{GL}(n)\). Zbl 0965.11023 Luo, Wenzhi; Rudnick, Zeév; Sarnak, Peter 99 1999 \(L^ \infty\) norms of eigenfunctions of arithmetic surfaces. Zbl 0833.11019 Iwaniec, H.; Sarnak, P. 93 1995 Perspectives on the analytic theory of \(L\)-functions. Special volume of the journal Geometric and Functional Analysis. Zbl 0996.11036 Iwaniec, H.; Sarnak, P. 90 2000 Affine linear sieve, expanders, and sum-product. Zbl 1239.11103 Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 88 2010 Chebyshev’s bias. Zbl 0823.11050 Rubinstein, Michael; Sarnak, Peter 86 1994 Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\). Zbl 0852.11024 Luo, Wenzhi; Sarnak, Peter 83 1995 Disjointness of Moebius from horocycle flows. Zbl 1336.37030 Bourgain, J.; Sarnak, P.; Ziegler, T. 82 2013 The non-vanishing of central values of automorphic \(L\)-functions and Landau-Siegel zeros. Zbl 0992.11037 Iwaniec, Henryk; Sarnak, Peter 81 2000 Class numbers of indefinite binary quadratic forms. Zbl 0499.10021 Sarnak, Peter 80 1982 On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\). Zbl 0558.10017 Phillips, R. S.; Sarnak, P. 80 1985 Bounds for multiplicities of automorphic representations. Zbl 0741.22010 Sarnak, Peter; Xue, Xiaoxi 79 1991 On the period matrix of a Riemann surface of large genus (with an appendix by J. H. Conway and N. J. A. Sloane). Zbl 0814.14033 Buser, P.; Sarnak, P. 78 1994 Estimates for Rankin-Selberg \(L\)-functions and quantum unique ergodicity. Zbl 1006.11022 Sarnak, Peter 73 2001 Arithmetic quantum chaos. Zbl 0831.58045 Sarnak, Peter 70 1995 Möbius randomness and dynamics. Zbl 1473.11147 Sarnak, Peter 70 2012 Compact isospectral sets of surfaces. Zbl 0653.53021 Osgood, B.; Phillips, R.; Sarnak, P. 69 1988 Heegner points, cycles and Maass forms. Zbl 0787.11016 Katok, Svetlana; Sarnak, Peter 69 1993 The arithmetic and geometry of some hyperbolic three manifolds. Zbl 0527.10022 Sarnak, P. 67 1983 Generalization of Selberg’s \(\frac {3}{16} \) theorem and affine sieve. Zbl 1276.11081 Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 64 2011 Asymptotic behavior of periodic orbits of the horocycle flow and Eisenstein series. Zbl 0501.58027 Sarnak, Peter 63 1981 Hecke operators and distributing points on the sphere. I. Zbl 0619.10052 Lubotzky, A.; Phillips, R.; Sarnak, P. 62 1986 The pair correlation function of fractional parts of polynomials. Zbl 0919.11052 Rudnick, Zeév; Sarnak, Peter 62 1998 Minima of Epstein’s zeta function and heights of flat tori. Zbl 1145.11033 Sarnak, Peter; Strömbergsson, Andreas 59 2006 Notes on the generalized Ramanujan conjectures. Zbl 1146.11031 Sarnak, Peter 55 2005 Ramanujan duals. II. Zbl 0774.11021 Burger, Marc; Sarnak, P. 52 1991 Hecke operators and distributing points on \(S^2\). II. Zbl 0648.10034 Lubotzky, A.; Phillips, R.; Sarnak, P. 51 1987 The distribution of spacings between the fractional parts of \(n^2\alpha\). Zbl 1006.11041 Rudnick, Zeév; Sarnak, Peter; Zaharescu, Alexandru 50 2001 Sums of Kloosterman sums. Zbl 0507.10029 Goldfeld, D.; Sarnak, P. 49 1983 Spectra of hyperbolic surfaces. Zbl 1045.11033 Sarnak, Peter 48 2003 The Möbius function and distal flows. Zbl 1383.11094 Liu, Jianya; Sarnak, Peter 45 2015 Geodesics in homology classes. Zbl 0642.53050 Phillips, Ralph; Sarnak, Peter 44 1987 Statistical properties of eigenvalues of the Hecke operators. Zbl 0628.10028 Sarnak, Peter 42 1987 Integrals of products of eigenfunctions. Zbl 0833.11020 Sarnak, Peter 38 1994 Sieving and expanders. Zbl 1217.11081 Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 37 2006 Families of \(L\)-functions and their symmetry. Zbl 1417.11078 Sarnak, Peter; Shin, Sug Woo; Templier, Nicolas 37 2016 The horocycle flow at prime times. Zbl 1307.11048 Sarnak, Peter; Ubis, Adrián 35 2015 Spectra of elements in the group ring of SU(2). Zbl 0916.22009 Gamburd, Alex; Jakobson, Dmitry; Sarnak, Peter 35 1999 Nodal domains of Maass forms. I. Zbl 1328.11044 Ghosh, Amit; Reznikov, Andre; Sarnak, Peter 34 2013 Diophantine problems and linear groups. Zbl 0743.11018 Sarnak, Peter C. 33 1991 Notes on thin matrix groups. Zbl 1365.11039 Sarnak, Peter 33 2014 Spectral behavior of quasi periodic potentials. Zbl 0506.35074 Sarnak, P. 31 1982 Determinants of Laplacians; heights and finiteness. Zbl 0703.53037 Sarnak, Peter 30 1990 What is …an expander? Zbl 1161.05341 Sarnak, Peter 30 2004 Dirichlet \(L\)-functions at the central point. Zbl 0929.11025 Iwaniec, H.; Sarnak, P. 30 1999 Recent progress on the quantum unique ergodicity conjecture. Zbl 1234.58007 Sarnak, Peter 29 2011 Integral Apollonian packings. Zbl 1260.52011 Sarnak, Peter 28 2011 Markoff triples and strong approximation. (Triplets de Markoff et approximation forte.) Zbl 1378.11043 Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter 28 2016 Mass equidistribution for Hecke eigenforms. Zbl 1044.11022 Luo, Wenzhi; Sarnak, Peter 28 2003 Values at integers of binary quadratic forms. Zbl 0911.11032 Sarnak, Peter 27 1997 Topologies of nodal sets of random band-limited functions. Zbl 1414.58019 Sarnak, Peter; Wigman, Igor 26 2019 The Laplacian for domains in hyperbolic space and limit sets of Kleinian groups. Zbl 0611.30037 Phillips, R. S.; Sarnak, P. 25 1985 Reciprocal geodesics. Zbl 1198.11039 Sarnak, Peter 25 2007 Topology and nesting of the zero set components of monochromatic random waves. Zbl 1473.60095 Canzani, Yaiza; Sarnak, Peter 25 2019 Perturbation theory for the Laplacian on automorphic functions. Zbl 0743.30039 Phillips, R.; Sarnak, P. 24 1992 Betti numbers of congruence groups. (Appendix: On representations of compact \(p\)-adic groups by Ze’ev Rudnick). Zbl 0843.11027 Sarnak, Peter; Adams, Scot 24 1994 Number variance for arithmetic hyperbolic surfaces. Zbl 0797.58069 Luo, W.; Sarnak, P. 24 1994 Ramanujan duals and automorphic spectrum. Zbl 0762.22009 Burger, Marc; Li, J. S.; Sarnak, P. 24 1992 The Weyl theorem and the deformation of discrete groups. Zbl 0614.10027 Phillips, R. S.; Sarnak, P. 24 1985 Real zeros of holomorphic Hecke cusp forms. Zbl 1287.11054 Ghosh, Amit; Sarnak, Peter 24 2012 Prime and almost prime integral points on principal homogeneous spaces. Zbl 1233.11102 Nevo, Amos; Sarnak, Peter 24 2010 Topologies of nodal sets of random band limited functions. Zbl 1366.60015 Sarnak, Peter; Wigman, Igor 24 2016 Moduli space, heights and isospectral sets of plane domains. Zbl 0677.58045 Osgood, B.; Phillips, R.; Sarnak, P. 23 1989 Selberg’s eigenvalue conjecture. Zbl 1042.11517 Sarnak, Peter 23 1995 Quantum variance for Hecke eigenforms. Zbl 1121.11042 Luo, Wenzhi; Sarnak, Peter 20 2004 On Linnik and Selberg’s conjecture about sums of Kloosterman sums. Zbl 1234.11104 Sarnak, Peter; Tsimerman, Jacob 19 2009 Sector estimates for hyperbolic isometries. Zbl 1208.22007 Bourgain, Jean; Kontorovich, Alex; Sarnak, Peter 19 2010 Additive number theory and Maass forms. Zbl 0534.10021 Sarnak, Peter 18 1984 Maass cusp forms. Zbl 0566.10017 Deshouillers, J.-M.; Iwaniec, H.; Phillips, R. S.; Sarnak, P. 18 1985 The affine sieve. Zbl 1283.20055 Salehi Golsefidy, Alireza; Sarnak, Peter 18 2013 Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions. Zbl 1347.20054 Fuchs, Elena; Meiri, Chen; Sarnak, Peter 18 2014 Fourth moments of Grössencharakteren zeta functions. Zbl 0577.10026 Sarnak, Peter 17 1985 Zeros of L-functions attached to Maass forms. Zbl 0565.10026 Epstein, Charles; Hafner, James Lee; Sarnak, Peter 17 1985 Quantum unique ergodicity for \(\text{SL}_2 (\mathcal O)\backslash\mathbb{H}^3\) and estimates for \(L\)-functions. Zbl 0995.11036 Petridis, Yiannis; Sarnak, Peter 17 2001 Super-Golden-Gates for \(PU(2)\). Zbl 1383.81059 Parzanchevski, Ori; Sarnak, Peter 17 2018 The spectrum of Fermat curves. Zbl 0751.11030 Phillips, R.; Sarnak, P. 16 1991 Integral points on quadrics in three variables whose coordinates have few prime factors. Zbl 1230.11045 Liu, Jianya; Sarnak, Peter 16 2010 Local statistics of lattice points on the sphere. Zbl 1394.11059 Bourgain, Jean; Sarnak, Peter; Rudnick, Zeév 15 2016 Nonvanishing of \(L\)-functions on \(\operatorname{Re}(s)=1\). Zbl 1088.11067 Sarnak, Peter 15 2004 Stable polynomials and crystalline measures. Zbl 1459.05177 Kurasov, P.; Sarnak, P. 15 2020 Poincaré series for \(SO(n,1)\). Zbl 0743.11028 Cogdell, J.; Li, J.-S.; Piatetski-Shapiro, Ilya I.; Sarnak, P. 14 1991 Strong spectral gaps for compact quotients of products of \(\text{PSL}(2,\mathbb R)\). Zbl 1254.11050 Kelmer, Dubi; Sarnak, Peter 14 2009 A new curvature invariant and entropy of geodesic flows. Zbl 0536.53048 Osserman, R.; Sarnak, P. 14 1984 Class numbers of indefinite binary quadratic forms. II. Zbl 0571.10022 Sarnak, Peter C. 14 1985 Line-graph lattices: Euclidean and non-Euclidean flat bands, and implementations in circuit quantum electrodynamics. Zbl 1481.81007 Kollár, Alicia J.; Fitzpatrick, Mattias; Sarnak, Peter; Houck, Andrew A. 14 2020 The \(n\)-level correlations of zeros of the zeta function. Zbl 0837.11047 Rudnick, Zeév; Sarnak, Peter 13 1994 The determinant of the Eisenstein matrix and Hilbert class fields. Zbl 0576.10017 Efrat, I.; Sarnak, P. 13 1985 A proof of Siegel’s weight formula. Zbl 0743.11023 Eskin, Alex; Rudnick, Zeév; Sarnak, Peter 11 1991 Integral points on Markoff type cubic surfaces. Zbl 1510.11088 Ghosh, Amit; Sarnak, Peter 2 2022 Gap sets for the spectra of cubic graphs. Zbl 1531.05151 Kollár, Alicia J.; Sarnak, Peter 5 2021 Commutators in \(\mathrm{SL}_2\) and Markoff surfaces. I. Zbl 1517.20041 Ghosh, Amit; Meiri, Chen; Sarnak, Peter 2 2021 Stable polynomials and crystalline measures. Zbl 1459.05177 Kurasov, P.; Sarnak, P. 15 2020 Line-graph lattices: Euclidean and non-Euclidean flat bands, and implementations in circuit quantum electrodynamics. Zbl 1481.81007 Kollár, Alicia J.; Fitzpatrick, Mattias; Sarnak, Peter; Houck, Andrew A. 14 2020 Topologies of nodal sets of random band-limited functions. Zbl 1414.58019 Sarnak, Peter; Wigman, Igor 26 2019 Topology and nesting of the zero set components of monochromatic random waves. Zbl 1473.60095 Canzani, Yaiza; Sarnak, Peter 25 2019 The quantum variance of the modular surface. Zbl 1455.11076 Sarnak, P.; Zhao, P. 5 2019 Super-Golden-Gates for \(PU(2)\). Zbl 1383.81059 Parzanchevski, Ori; Sarnak, Peter 17 2018 Maryam Mirzakhani: 1977–2017. Zbl 1404.01038 Beheshti, Roya; Coskun, Izzet; DeMarco, Laura; Dumas, David; Lindenstrauss, Elon; Sarnak, Peter; Eskin, Alex; Sapir, Eugenia; Barcelo, Hélène; Eisenbud, David; Hamenstädt, Ursula; Wolpert, Scott A.; Wright, Alex; Zorich, Anton 1 2018 Spatial statistics for lattice points on the sphere. I: Individual results. Zbl 1464.11076 Bourgain, Jean; Rudnick, Zeév; Sarnak, Peter 10 2017 Nodal domains of Maass forms. II. Zbl 1392.11026 Ghosh, Amit; Reznikov, Andre; Sarnak, Peter 8 2017 The Möbius disjointness conjecture for distal flows. Zbl 1432.11107 Liu, Jianya; Sarnak, Peter 5 2017 Families of \(L\)-functions and their symmetry. Zbl 1417.11078 Sarnak, Peter; Shin, Sug Woo; Templier, Nicolas 37 2016 Markoff triples and strong approximation. (Triplets de Markoff et approximation forte.) Zbl 1378.11043 Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter 28 2016 Topologies of nodal sets of random band limited functions. Zbl 1366.60015 Sarnak, Peter; Wigman, Igor 24 2016 Local statistics of lattice points on the sphere. Zbl 1394.11059 Bourgain, Jean; Sarnak, Peter; Rudnick, Zeév 15 2016 The Möbius function and distal flows. Zbl 1383.11094 Liu, Jianya; Sarnak, Peter 45 2015 The horocycle flow at prime times. Zbl 1307.11048 Sarnak, Peter; Ubis, Adrián 35 2015 Notes on thin matrix groups. Zbl 1365.11039 Sarnak, Peter 33 2014 Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions. Zbl 1347.20054 Fuchs, Elena; Meiri, Chen; Sarnak, Peter 18 2014 Disjointness of Moebius from horocycle flows. Zbl 1336.37030 Bourgain, J.; Sarnak, P.; Ziegler, T. 82 2013 Nodal domains of Maass forms. I. Zbl 1328.11044 Ghosh, Amit; Reznikov, Andre; Sarnak, Peter 34 2013 The affine sieve. Zbl 1283.20055 Salehi Golsefidy, Alireza; Sarnak, Peter 18 2013 Möbius randomness and dynamics. Zbl 1473.11147 Sarnak, Peter 70 2012 Real zeros of holomorphic Hecke cusp forms. Zbl 1287.11054 Ghosh, Amit; Sarnak, Peter 24 2012 Recent progress on the quantum unique ergodicity conjecture. Zbl 1317.58036 Sarnak, Peter 3 2012 Generalization of Selberg’s \(\frac {3}{16} \) theorem and affine sieve. Zbl 1276.11081 Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 64 2011 Recent progress on the quantum unique ergodicity conjecture. Zbl 1234.58007 Sarnak, Peter 29 2011 Integral Apollonian packings. Zbl 1260.52011 Sarnak, Peter 28 2011 Affine linear sieve, expanders, and sum-product. Zbl 1239.11103 Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 88 2010 Prime and almost prime integral points on principal homogeneous spaces. Zbl 1233.11102 Nevo, Amos; Sarnak, Peter 24 2010 Sector estimates for hyperbolic isometries. Zbl 1208.22007 Bourgain, Jean; Kontorovich, Alex; Sarnak, Peter 19 2010 Integral points on quadrics in three variables whose coordinates have few prime factors. Zbl 1230.11045 Liu, Jianya; Sarnak, Peter 16 2010 Linking numbers of modular knots. Zbl 1206.57011 Sarnak, Peter 4 2010 The Grand Riemann Hypothesis. (Extended abstract). Zbl 1275.11121 Sarnak, Peter 1 2010 On Linnik and Selberg’s conjecture about sums of Kloosterman sums. Zbl 1234.11104 Sarnak, Peter; Tsimerman, Jacob 19 2009 Strong spectral gaps for compact quotients of products of \(\text{PSL}(2,\mathbb R)\). Zbl 1254.11050 Kelmer, Dubi; Sarnak, Peter 14 2009 The variance of arithmetic measures associated to closed geodesics on the modular surface. Zbl 1231.11057 Luo, Wenzhi; Rudnick, Zeév; Sarnak, Peter 9 2009 Equidistribution and primes. Zbl 1223.11112 Sarnak, Peter 10 2008 Some applications of modular forms. Paperback reprint. Zbl 1141.11023 Sarnak, Peter 3 2008 Some commentary on Atle Selberg’s mathematics. Zbl 1144.01301 Hejhal, D.; Sarnak, P. 2 2008 Reciprocal geodesics. Zbl 1198.11039 Sarnak, Peter 25 2007 Automorphic forms and applications. Papers of the IAS/Park City Mathematics Institute, Park City, UT, USA, July 1–20, 2002. Zbl 1116.11003 5 2007 Minima of Epstein’s zeta function and heights of flat tori. Zbl 1145.11033 Sarnak, Peter; Strömbergsson, Andreas 59 2006 Sieving and expanders. Zbl 1217.11081 Bourgain, Jean; Gamburd, Alex; Sarnak, Peter 37 2006 Notes on the generalized Ramanujan conjectures. Zbl 1146.11031 Sarnak, Peter 55 2005 Selected papers. Vols. I, II. Edited by Peter Sarnak and Andrew Majda. Zbl 1087.01018 Lax, Peter D. 2 2005 What is …an expander? Zbl 1161.05341 Sarnak, Peter 30 2004 Quantum variance for Hecke eigenforms. Zbl 1121.11042 Luo, Wenzhi; Sarnak, Peter 20 2004 Nonvanishing of \(L\)-functions on \(\operatorname{Re}(s)=1\). Zbl 1088.11067 Sarnak, Peter 15 2004 A new method for lower bounds of \(L\)-functions. Zbl 1101.11034 Gelbart, Stephen S.; Lapid, Erez M.; Sarnak, Peter 9 2004 Functoriality for the exterior square of \(\text{GL}_4\) and the symmetric fourth of \(\text{GL}_2\). Appendix 1 by Dinakar Ramakrishnan, Appendix 2 by Henry H. Kim and Peter Sarnak. Zbl 1018.11024 Kim, Henry H. 438 2003 Elementary number theory, group theory and Ramanujan graphs. Zbl 1032.11001 Davidoff, Giuliana; Sarnak, Peter; Valette, Alain 122 2003 Spectra of hyperbolic surfaces. Zbl 1045.11033 Sarnak, Peter 48 2003 Mass equidistribution for Hecke eigenforms. Zbl 1044.11022 Luo, Wenzhi; Sarnak, Peter 28 2003 Arithmetic and equidistribution of measures on the sphere. Zbl 1090.11033 Böcherer, Siegfried; Sarnak, Peter; Schulze-Pillot, Rainer 6 2003 Maass cusp forms with integer coefficients. Zbl 1035.11023 Sarnak, Peter 4 2002 Some remarks on Landau-Siegel zeros. Zbl 1008.11033 Sarnak, P.; Zaharescu, A. 3 2002 Estimates for Rankin-Selberg \(L\)-functions and quantum unique ergodicity. Zbl 1006.11022 Sarnak, Peter 73 2001 The distribution of spacings between the fractional parts of \(n^2\alpha\). Zbl 1006.11041 Rudnick, Zeév; Sarnak, Peter; Zaharescu, Alexandru 50 2001 Quantum unique ergodicity for \(\text{SL}_2 (\mathcal O)\backslash\mathbb{H}^3\) and estimates for \(L\)-functions. Zbl 0995.11036 Petridis, Yiannis; Sarnak, Peter 17 2001 Low lying zeros of families of \(L\)-functions. Zbl 1012.11041 Iwaniec, Henryk; Luo, Wenzhi; Sarnak, Peter 200 2000 Perspectives on the analytic theory of \(L\)-functions. Special volume of the journal Geometric and Functional Analysis. Zbl 0996.11036 Iwaniec, H.; Sarnak, P. 90 2000 The non-vanishing of central values of automorphic \(L\)-functions and Landau-Siegel zeros. Zbl 0992.11037 Iwaniec, Henryk; Sarnak, Peter 81 2000 Kloosterman, quadratic forms and modular forms. Zbl 1173.11341 Sarnak, Peter 3 2000 Selected works of Ilya Piatetski-Shapiro. Edited by James Cogdell, Simon Gindikin and Peter Sarnak. Zbl 0958.01046 Piatetski-Shapiro, Ilya 2 2000 Random matrices, Frobenius eigenvalues, and monodromy. Zbl 0958.11004 Katz, Nicholas M.; Sarnak, Peter 289 1999 Zeroes of zeta functions and symmetry. Zbl 0921.11047 Katz, Nicholas M.; Sarnak, Peter 177 1999 On the generalized Ramanujan conjecture for \(\text{GL}(n)\). Zbl 0965.11023 Luo, Wenzhi; Rudnick, Zeév; Sarnak, Peter 99 1999 Spectra of elements in the group ring of SU(2). Zbl 0916.22009 Gamburd, Alex; Jakobson, Dmitry; Sarnak, Peter 35 1999 Dirichlet \(L\)-functions at the central point. Zbl 0929.11025 Iwaniec, H.; Sarnak, P. 30 1999 Equidistribution of holonomy about closed geodesics. Zbl 0939.22008 Sarnak, Peter; Wakayama, Masato 8 1999 Quantum chaos, symmetry and zeta functions. Lecture I: Quantum chaos, Lecture II: Zeta functions. Zbl 0954.11018 Sarnak, Peter 5 1999 The pair correlation function of fractional parts of polynomials. Zbl 0919.11052 Rudnick, Zeév; Sarnak, Peter 62 1998 \(L\)-functions. Zbl 0930.11065 Sarnak, Peter 4 1998 Values at integers of binary quadratic forms. Zbl 0911.11032 Sarnak, Peter 27 1997 Extremal geometries. Zbl 0873.58069 Sarnak, Peter 9 1997 Extremal Riemann surfaces. From the proceedings of the AMS special session with related papers, January 4–5, 1995, San Francisco, CA, USA. Zbl 0856.00021 3 1997 Spectra and eigenfunctions of Laplacians. Zbl 0888.58069 Sarnak, Peter 1 1997 Zeros of principal \(L\)-functions and random matrix theory. Zbl 0866.11050 Rudnick, Zeév; Sarnak, Peter 231 1996 On Selberg’s eigenvalue conjecture. Zbl 0844.11038 Luo, W.; Rudnick, Z.; Sarnak, P. 100 1995 \(L^ \infty\) norms of eigenfunctions of arithmetic surfaces. Zbl 0833.11019 Iwaniec, H.; Sarnak, P. 93 1995 Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\). Zbl 0852.11024 Luo, Wenzhi; Sarnak, Peter 83 1995 Arithmetic quantum chaos. Zbl 0831.58045 Sarnak, Peter 70 1995 Selberg’s eigenvalue conjecture. Zbl 1042.11517 Sarnak, Peter 23 1995 Some hypersurfaces in \(\mathbb{P}^ 4\) and the Hasse-principle. Zbl 0857.14013 Sarnak, Peter; Wang, Lan 8 1995 The behaviour of eigenstates of arithmetic hyperbolic manifolds. Zbl 0836.58043 Rudnick, Zeév; Sarnak, Peter 134 1994 Chebyshev’s bias. Zbl 0823.11050 Rubinstein, Michael; Sarnak, Peter 86 1994 On the period matrix of a Riemann surface of large genus (with an appendix by J. H. Conway and N. J. A. Sloane). Zbl 0814.14033 Buser, P.; Sarnak, P. 78 1994 Integrals of products of eigenfunctions. Zbl 0833.11020 Sarnak, Peter 38 1994 Betti numbers of congruence groups. (Appendix: On representations of compact \(p\)-adic groups by Ze’ev Rudnick). Zbl 0843.11027 Sarnak, Peter; Adams, Scot 24 1994 Number variance for arithmetic hyperbolic surfaces. Zbl 0797.58069 Luo, W.; Sarnak, P. 24 1994 The \(n\)-level correlations of zeros of the zeta function. Zbl 0837.11047 Rudnick, Zeév; Sarnak, Peter 13 1994 Cusp forms for character varieties. Zbl 0804.11038 Phillips, R.; Sarnak, P. 8 1994 Density of integer points on affine homogeneous varieties. Zbl 0798.11024 Duke, W.; Rudnick, Z.; Sarnak, P. 138 1993 Heegner points, cycles and Maass forms. Zbl 0787.11016 Katok, Svetlana; Sarnak, Peter 69 1993 Relatively prime values of polynomials. Zbl 0790.11069 Hafner, James Lee; Sarnak, Peter; McCurley, Kevin 1 1993 Perturbation theory for the Laplacian on automorphic functions. Zbl 0743.30039 Phillips, R.; Sarnak, P. 24 1992 Ramanujan duals and automorphic spectrum. Zbl 0762.22009 Burger, Marc; Li, J. S.; Sarnak, P. 24 1992 ...and 47 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,369 Authors 65 Sarnak, Peter Clive 43 Bourgain, Jean 41 Blomer, Valentin 30 Zaharescu, Alexandru 28 Miller, Steven J. 27 Kontorovich, Alex V. 26 Lu, Guangshi 24 Michel, Philippe Gabriel 24 Rudnick, Zeév 23 Ye, Yangbo 22 Kowalski, Emmanuel 20 Bétermin, Laurent 20 Oh, Hee 20 Shparlinski, Igor E. 19 Gorodnik, Alexander 19 Jorgenson, Jay Alan 19 Lemańczyk, Mariusz 19 Young, Matthew P. 18 Gamburd, Alexander 17 Alon, Noga 17 Keating, Jonathan Peter 17 Smajlović, Lejla 16 Lubotzky, Alexander 15 Jiang, Yujiao 15 Radziwiłł, Maksym 15 Templier, Nicolas 15 Zelditch, Steve 14 Kelmer, Dubi 14 Khan, Rizwanur 14 Koyama, Shin-ya 14 Lau, Yuk-Kam 14 Liu, Jianya 14 Soundararajan, Kannan 13 Duke, William Drexel 13 Harcos, Gergely 13 Kułaga-Przymus, Joanna 13 Liu, Sheng-Chi 13 Luo, Wenzhi 13 Nevo, Amos 13 Sun, Qingfeng 12 Balkanova, Ol’ga Germanovna 12 Frolenkov, Dmitriĭ Andreevich 12 Huang, Bingrong 12 Katz, Nicholas Michael 12 Linial, Nathan 12 Marklof, Jens 12 Nelson, Paul D. 12 Petridis, Yiannis N. 12 Pollicott, Mark 12 Venkatesh, Akshay 12 Wu, Jie 11 Choi, Junesang 11 Conrey, John Brian 11 Hua, Guodong 11 Kim, Henry H. 11 Lao, Huixue 11 Lindenstrauss, Elon 11 Mohammadi, Amir 11 Phillips, Ralph Saul 11 Södergren, Anders 11 Wigderson, Avi 11 Zhao, Liangyi 10 Aistleitner, Christoph 10 Deitmar, Anton 10 Einsiedler, Manfred Leopold 10 Gao, Peng 10 Humphries, Peter J. 10 Iwaniec, Henryk 10 Kurlberg, Pär 10 Magee, Michael 10 Milićević, Djordje 10 Petrow, Ian N. 10 Rivière, Gabriel 10 Tang, Hengcai 10 Wigman, Igor 9 Anantharaman, Nalini 9 Andrade, Julio Cesar 9 Bui, Hung Manh 9 Canzani, Yaiza 9 Chandee, Vorrapan 9 Chang, Sun-Yung Alice 9 Dyatlov, Semyon 9 Fouvry, Etienne 9 Gillespie, Timothy L. 9 Gun, Sanoli 9 Jakobson, Dmitry 9 Lapid, Erez Moshe 9 Maga, Péter 9 Paulin, Frédéric 9 Salehi Golsefidy, Alireza 9 Sawin, William F. 9 Shah, Nimish A. 9 Sharp, Richard W. 9 Shkredov, Il’ya Dmitrievich 9 Snaith, Nina Claire 9 Steinerberger, Stefan 9 Wu, Yunhui 8 Avdispahić, Muharem 8 Bergeron, Nicolas 8 Branson, Thomas Patrick ...and 3,269 more Authors all top 5 Cited in 404 Serials 228 Journal of Number Theory 164 Duke Mathematical Journal 113 Communications in Mathematical Physics 91 Transactions of the American Mathematical Society 88 Advances in Mathematics 83 Proceedings of the American Mathematical Society 76 Israel Journal of Mathematics 73 Mathematische Zeitschrift 66 Inventiones Mathematicae 65 Geometric and Functional Analysis. 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Quatrième Série 8 Publications Mathématiques 8 Journal of Computational and Applied Mathematics 8 Mathematische Nachrichten 8 Results in Mathematics ...and 304 more Serials all top 5 Cited in 59 Fields 2,157 Number theory (11-XX) 496 Combinatorics (05-XX) 455 Global analysis, analysis on manifolds (58-XX) 423 Dynamical systems and ergodic theory (37-XX) 295 Topological groups, Lie groups (22-XX) 266 Probability theory and stochastic processes (60-XX) 249 Partial differential equations (35-XX) 247 Algebraic geometry (14-XX) 237 Differential geometry (53-XX) 229 Quantum theory (81-XX) 228 Group theory and generalizations (20-XX) 179 Computer science (68-XX) 158 Functions of a complex variable (30-XX) 134 Linear and multilinear algebra; matrix theory (15-XX) 91 Manifolds and cell complexes (57-XX) 90 Operator theory (47-XX) 85 Special functions (33-XX) 85 Statistical mechanics, structure of matter (82-XX) 82 Several complex variables and analytic spaces (32-XX) 79 Information and communication theory, circuits (94-XX) 74 Measure and integration (28-XX) 73 Convex and discrete geometry (52-XX) 70 Functional analysis (46-XX) 56 Harmonic analysis on Euclidean spaces (42-XX) 52 Abstract harmonic analysis (43-XX) 39 Ordinary differential equations (34-XX) 37 Geometry (51-XX) 31 Relativity and gravitational theory (83-XX) 28 Numerical analysis (65-XX) 27 Approximations and expansions (41-XX) 25 Operations research, mathematical programming (90-XX) 20 Statistics (62-XX) 19 Real functions (26-XX) 17 General and overarching topics; collections (00-XX) 16 Potential theory (31-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 15 Algebraic topology (55-XX) 14 Mathematical logic and foundations (03-XX) 14 Nonassociative rings and algebras (17-XX) 13 General topology (54-XX) 11 Difference and functional equations (39-XX) 11 Mechanics of deformable solids (74-XX) 10 Biology and other natural sciences (92-XX) 9 Commutative algebra (13-XX) 9 Integral transforms, operational calculus (44-XX) 9 Mechanics of particles and systems (70-XX) 7 Associative rings and algebras (16-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 History and biography (01-XX) 6 Order, lattices, ordered algebraic structures (06-XX) 6 Field theory and polynomials (12-XX) 6 Sequences, series, summability (40-XX) 5 \(K\)-theory (19-XX) 4 Fluid mechanics (76-XX) 3 Integral equations (45-XX) 2 Optics, electromagnetic theory (78-XX) 2 Systems theory; control (93-XX) 1 General algebraic systems (08-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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