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Sarnak, Peter Clive

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Author ID: sarnak.peter-c Recent zbMATH articles by "Sarnak, Peter Clive"
Published as: Sarnak, Peter; Sarnak, P.; Sarnak, Peter C.
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
Awards: Wolf Prize (2014)
all top 5

Co-Authors

54 single-authored
17 Phillips, Ralph Saul
13 Rudnick, Zeév
8 Bourgain, Jean
8 Luo, Wenzhi
6 Iwaniec, Henryk
5 Gamburd, Alexander
4 Gelbart, Stephen S.
4 Ghosh, Amit
4 Osgood, Brad G.
3 Cogdell, James W.
3 Hejhal, Dennis A.
3 Howe, Roger Evans
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
2 Burger, Marc
2 Eskin, Alex
2 Gindikin, Simon Grigorevich
2 Hafner, James Lee
2 Jakobson, Dmitry
2 Katz, Nicholas Michael
2 Kontorovich, Alex V.
2 Kuhn, Harold William
2 Meiri, Chen
2 Nirenberg, Louis
2 Reznikov, Andre
2 Shahidi, Freydoon
2 Weisfeld, Morris
2 Wigman, Igor
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 Canzani, Yaiza
1 Cohen, Charles J.
1 Conway, John Horton
1 Coskun, Izzet
1 Daubechies, Ingrid Chantal
1 Davidoff, Giuliana
1 Delbaen, Freddy
1 DeMarco, Laura Grace
1 Deshouillers, Jean-Marc
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 Ilyashenko, Yulij Sergeevich
1 Jacquet, Hervé Michel
1 Jitomirskaya, Svetlana Yakovlevna
1 Katok, Svetlana R.
1 Kelmer, Dubi
1 Kenig, Carlos Eduardo
1 Kennedy, Stephen F.
1 Kim, Henry H.
1 Klainerman, Sergiu
1 Kollár, Alicia J.
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 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.
1 Rubinstein, Michael O.
1 Salehi Golsefidy, Alireza
1 Sapir, Eugenia
1 Schlag, Wilhelm
...and 28 more Co-Authors
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Serials

10 Duke Mathematical Journal
9 Notices of the American Mathematical Society
8 Communications on Pure and Applied Mathematics
8 Inventiones Mathematicae
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 the European Mathematical Society (JEMS)
3 Journal of Number Theory
3 Journal of the American Mathematical Society
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
2 Publications Mathématiques
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 Contemporary 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 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 Combinatorica
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

Publications by Year

Citations contained in zbMATH Open

144 Publications have been cited 4,776 times in 2,924 Documents Cited by Year
Ramanujan graphs. Zbl 0661.05035
Lubotzky, A.; Phillips, R.; Sarnak, P.
384
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.
224
2003
Random matrices, Frobenius eigenvalues, and monodromy. Zbl 0958.11004
Katz, Nicholas M.; Sarnak, Peter
214
1999
Extremals of determinants of Laplacians. Zbl 0653.53022
Osgood, B.; Phillips, R.; Sarnak, P.
185
1988
Zeros of principal \(L\)-functions and random matrix theory. Zbl 0866.11050
Rudnick, Zeév; Sarnak, Peter
177
1996
Low lying zeros of families of \(L\)-functions. Zbl 1012.11041
Iwaniec, Henryk; Luo, Wenzhi; Sarnak, Peter
149
2000
Zeroes of zeta functions and symmetry. Zbl 0921.11047
Katz, Nicholas M.; Sarnak, Peter
124
1999
Density of integer points on affine homogeneous varieties. Zbl 0798.11024
Duke, W.; Rudnick, Z.; Sarnak, P.
113
1993
The behaviour of eigenstates of arithmetic hyperbolic manifolds. Zbl 0836.58043
Rudnick, Zeév; Sarnak, Peter
103
1994
Determinants of Laplacians. Zbl 0618.10023
Sarnak, Peter
99
1987
Elementary number theory, group theory and Ramanujan graphs. Zbl 1032.11001
Davidoff, Giuliana; Sarnak, Peter; Valette, Alain
89
2003
On Selberg’s eigenvalue conjecture. Zbl 0844.11038
Luo, W.; Rudnick, Z.; Sarnak, P.
82
1995
Some applications of modular forms. Zbl 0721.11015
Sarnak, Peter
80
1990
On the generalized Ramanujan conjecture for \(\text{GL}(n)\). Zbl 0965.11023
Luo, Wenzhi; Rudnick, Zeév; Sarnak, Peter
77
1999
\(L^ \infty\) norms of eigenfunctions of arithmetic surfaces. Zbl 0833.11019
Iwaniec, H.; Sarnak, P.
72
1995
On cusp forms for co-finite subgroups of PSL(2,\({\mathbb{R}})\). Zbl 0558.10017
Phillips, R. S.; Sarnak, P.
71
1985
Class numbers of indefinite binary quadratic forms. Zbl 0499.10021
Sarnak, Peter
71
1982
Perspectives on the analytic theory of \(L\)-functions. Special volume of the journal Geometric and Functional Analysis. Zbl 0996.11036
Iwaniec, H.; Sarnak, P.
69
2000
The non-vanishing of central values of automorphic \(L\)-functions and Landau-Siegel zeros. Zbl 0992.11037
Iwaniec, Henryk; Sarnak, Peter
68
2000
Chebyshev’s bias. Zbl 0823.11050
Rubinstein, Michael; Sarnak, Peter
64
1994
Heegner points, cycles and Maass forms. Zbl 0787.11016
Katok, Svetlana; Sarnak, Peter
64
1993
Affine linear sieve, expanders, and sum-product. Zbl 1239.11103
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
64
2010
Estimates for Rankin-Selberg \(L\)-functions and quantum unique ergodicity. Zbl 1006.11022
Sarnak, Peter
61
2001
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.
60
1994
Disjointness of Moebius from horocycle flows. Zbl 1336.37030
Bourgain, J.; Sarnak, P.; Ziegler, T.
59
2013
Bounds for multiplicities of automorphic representations. Zbl 0741.22010
Sarnak, Peter; Xue, Xiaoxi
59
1991
The arithmetic and geometry of some hyperbolic three manifolds. Zbl 0527.10022
Sarnak, P.
57
1983
Compact isospectral sets of surfaces. Zbl 0653.53021
Osgood, B.; Phillips, R.; Sarnak, P.
56
1988
Arithmetic quantum chaos. Zbl 0831.58045
Sarnak, Peter
56
1995
Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\). Zbl 0852.11024
Luo, Wenzhi; Sarnak, Peter
53
1995
Generalization of Selberg’s \(\frac {3}{16} \) theorem and affine sieve. Zbl 1276.11081
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
53
2011
Hecke operators and distributing points on the sphere. I. Zbl 0619.10052
Lubotzky, A.; Phillips, R.; Sarnak, P.
51
1986
Asymptotic behavior of periodic orbits of the horocycle flow and Eisenstein series. Zbl 0501.58027
Sarnak, Peter
49
1981
Minima of Epstein’s zeta function and heights of flat tori. Zbl 1145.11033
Sarnak, Peter; Strömbergsson, Andreas
44
2006
The pair correlation function of fractional parts of polynomials. Zbl 0919.11052
Rudnick, Zeév; Sarnak, Peter
43
1998
Sums of Kloosterman sums. Zbl 0507.10029
Goldfeld, D.; Sarnak, P.
42
1983
Notes on the generalized Ramanujan conjectures. Zbl 1146.11031
Sarnak, Peter
42
2005
Hecke operators and distributing points on \(S^2\). II. Zbl 0648.10034
Lubotzky, A.; Phillips, R.; Sarnak, P.
41
1987
The distribution of spacings between the fractional parts of \(n^2\alpha\). Zbl 1006.11041
Rudnick, Zeév; Sarnak, Peter; Zaharescu, Alexandru
40
2001
Spectra of hyperbolic surfaces. Zbl 1045.11033
Sarnak, Peter
39
2003
Ramanujan duals. II. Zbl 0774.11021
Burger, Marc; Sarnak, P.
39
1991
The Möbius function and distal flows. Zbl 1383.11094
Liu, Jianya; Sarnak, Peter
38
2015
Geodesics in homology classes. Zbl 0642.53050
Phillips, Ralph; Sarnak, Peter
35
1987
Sieving and expanders. Zbl 1217.11081
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
33
2006
Integrals of products of eigenfunctions. Zbl 0833.11020
Sarnak, Peter
31
1994
Spectra of elements in the group ring of SU(2). Zbl 0916.22009
Gamburd, Alex; Jakobson, Dmitry; Sarnak, Peter
27
1999
Nodal domains of Maass forms. I. Zbl 1328.11044
Ghosh, Amit; Reznikov, Andre; Sarnak, Peter
27
2013
Mass equidistribution for Hecke eigenforms. Zbl 1044.11022
Luo, Wenzhi; Sarnak, Peter
25
2003
What is …an expander? Zbl 1161.05341
Sarnak, Peter
24
2004
Recent progress on the quantum unique ergodicity conjecture. Zbl 1234.58007
Sarnak, Peter
24
2011
Diophantine problems and linear groups. Zbl 0743.11018
Sarnak, Peter C.
23
1991
The Weyl theorem and the deformation of discrete groups. Zbl 0614.10027
Phillips, R. S.; Sarnak, P.
22
1985
The horocycle flow at prime times. Zbl 1307.11048
Sarnak, Peter; Ubis, Adrián
22
2015
Perturbation theory for the Laplacian on automorphic functions. Zbl 0743.30039
Phillips, R.; Sarnak, P.
22
1992
The Laplacian for domains in hyperbolic space and limit sets of Kleinian groups. Zbl 0611.30037
Phillips, R. S.; Sarnak, P.
21
1985
Number variance for arithmetic hyperbolic surfaces. Zbl 0797.58069
Luo, W.; Sarnak, P.
21
1994
Integral Apollonian packings. Zbl 1260.52011
Sarnak, Peter
21
2011
Prime and almost prime integral points on principal homogeneous spaces. Zbl 1233.11102
Nevo, Amos; Sarnak, Peter
21
2010
Dirichlet \(L\)-functions at the central point. Zbl 0929.11025
Iwaniec, H.; Sarnak, P.
20
1999
Selberg’s eigenvalue conjecture. Zbl 1042.11517
Sarnak, Peter
20
1995
Reciprocal geodesics. Zbl 1198.11039
Sarnak, Peter
20
2007
Real zeros of holomorphic Hecke cusp forms. Zbl 1287.11054
Ghosh, Amit; Sarnak, Peter
20
2012
Moduli space, heights and isospectral sets of plane domains. Zbl 0677.58045
Osgood, B.; Phillips, R.; Sarnak, P.
19
1989
Betti numbers of congruence groups. (Appendix: On representations of compact \(p\)-adic groups by Ze’ev Rudnick). Zbl 0843.11027
Sarnak, Peter; Adams, Scot
19
1994
Spectral behavior of quasi periodic potentials. Zbl 0506.35074
Sarnak, P.
19
1982
Notes on thin matrix groups. Zbl 1365.11039
Sarnak, Peter
19
2014
Families of \(L\)-functions and their symmetry. Zbl 1417.11078
Sarnak, Peter; Shin, Sug Woo; Templier, Nicolas
19
2016
Ramanujan duals and automorphic spectrum. Zbl 0762.22009
Burger, Marc; Li, J. S.; Sarnak, P.
19
1992
Topologies of nodal sets of random band limited functions. Zbl 1366.60015
Sarnak, Peter; Wigman, Igor
17
2016
Determinants of Laplacians; heights and finiteness. Zbl 0703.53037
Sarnak, Peter
17
1990
Values at integers of binary quadratic forms. Zbl 0911.11032
Sarnak, Peter
16
1997
Maass cusp forms. Zbl 0566.10017
Deshouillers, J.-M.; Iwaniec, H.; Phillips, R. S.; Sarnak, P.
16
1985
The affine sieve. Zbl 1283.20055
Salehi Golsefidy, Alireza; Sarnak, Peter
16
2013
Topology and nesting of the zero set components of monochromatic random waves. Zbl 1473.60095
Canzani, Yaiza; Sarnak, Peter
16
2019
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
16
2001
Quantum variance for Hecke eigenforms. Zbl 1121.11042
Luo, Wenzhi; Sarnak, Peter
16
2004
Fourth moments of Grössencharakteren zeta functions. Zbl 0577.10026
Sarnak, Peter
15
1985
Sector estimates for hyperbolic isometries. Zbl 1208.22007
Bourgain, Jean; Kontorovich, Alex; Sarnak, Peter
15
2010
Zeros of L-functions attached to Maass forms. Zbl 0565.10026
Epstein, Charles; Hafner, James Lee; Sarnak, Peter
14
1985
Integral points on quadrics in three variables whose coordinates have few prime factors. Zbl 1230.11045
Liu, Jianya; Sarnak, Peter
14
2010
A new curvature invariant and entropy of geodesic flows. Zbl 0536.53048
Osserman, R.; Sarnak, P.
13
1984
The spectrum of Fermat curves. Zbl 0751.11030
Phillips, R.; Sarnak, P.
13
1991
On Linnik and Selberg’s conjecture about sums of Kloosterman sums. Zbl 1234.11104
Sarnak, Peter; Tsimerman, Jacob
13
2009
Class numbers of indefinite binary quadratic forms. II. Zbl 0571.10022
Sarnak, Peter C.
12
1985
The determinant of the Eisenstein matrix and Hilbert class fields. Zbl 0576.10017
Efrat, I.; Sarnak, P.
12
1985
Topologies of nodal sets of random band-limited functions. Zbl 1414.58019
Sarnak, Peter; Wigman, Igor
12
2019
Poincaré series for \(SO(n,1)\). Zbl 0743.11028
Cogdell, J.; Li, J.-S.; Piatetski-Shapiro, Ilya I.; Sarnak, P.
12
1991
Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions. Zbl 1347.20054
Fuchs, Elena; Meiri, Chen; Sarnak, Peter
12
2014
Statistical properties of eigenvalues of the Hecke operators. Zbl 0628.10028
Sarnak, Peter
11
1987
Spectra of singular measures as multipliers on \(L^ p\). Zbl 0461.43007
Sarnak, Peter
11
1980
The \(n\)-level correlations of zeros of the zeta function. Zbl 0837.11047
Rudnick, Zeév; Sarnak, Peter
11
1994
Strong spectral gaps for compact quotients of products of \(\text{PSL}(2,\mathbb R)\). Zbl 1254.11050
Kelmer, Dubi; Sarnak, Peter
11
2009
Markoff triples and strong approximation. (Triplets de Markoff et approximation forte.) Zbl 1378.11043
Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter
10
2016
A proof of Siegel’s weight formula. Zbl 0743.11023
Eskin, Alex; Rudnick, Zeév; Sarnak, Peter
10
1991
Nonvanishing of \(L\)-functions on \(\operatorname{Re}(s)=1\). Zbl 1088.11067
Sarnak, Peter
9
2004
Local statistics of lattice points on the sphere. Zbl 1394.11059
Bourgain, Jean; Sarnak, Peter; Rudnick, Zeév
9
2016
Super-Golden-Gates for \(PU(2)\). Zbl 1383.81059
Parzanchevski, Ori; Sarnak, Peter
9
2018
Extremal geometries. Zbl 0873.58069
Sarnak, Peter
8
1997
A new method for lower bounds of \(L\)-functions. Zbl 1101.11034
Gelbart, Stephen S.; Lapid, Erez M.; Sarnak, Peter
8
2004
Equidistribution and primes. Zbl 1223.11112
Sarnak, Peter
8
2008
Stable polynomials and crystalline measures. Zbl 1459.05177
Kurasov, P.; Sarnak, P.
5
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.
2
2020
Topology and nesting of the zero set components of monochromatic random waves. Zbl 1473.60095
Canzani, Yaiza; Sarnak, Peter
16
2019
Topologies of nodal sets of random band-limited functions. Zbl 1414.58019
Sarnak, Peter; Wigman, Igor
12
2019
The quantum variance of the modular surface. Zbl 1455.11076
Sarnak, P.; Zhao, P.
1
2019
Super-Golden-Gates for \(PU(2)\). Zbl 1383.81059
Parzanchevski, Ori; Sarnak, Peter
9
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
Nodal domains of Maass forms. II. Zbl 1392.11026
Ghosh, Amit; Reznikov, Andre; Sarnak, Peter
6
2017
Spatial statistics for lattice points on the sphere. I: Individual results. Zbl 1464.11076
Bourgain, Jean; Rudnick, Zeév; Sarnak, Peter
5
2017
The Möbius disjointness conjecture for distal flows. Zbl 1432.11107
Liu, Jianya; Sarnak, Peter
3
2017
Families of \(L\)-functions and their symmetry. Zbl 1417.11078
Sarnak, Peter; Shin, Sug Woo; Templier, Nicolas
19
2016
Topologies of nodal sets of random band limited functions. Zbl 1366.60015
Sarnak, Peter; Wigman, Igor
17
2016
Markoff triples and strong approximation. (Triplets de Markoff et approximation forte.) Zbl 1378.11043
Bourgain, Jean; Gamburd, Alexander; Sarnak, Peter
10
2016
Local statistics of lattice points on the sphere. Zbl 1394.11059
Bourgain, Jean; Sarnak, Peter; Rudnick, Zeév
9
2016
The Möbius function and distal flows. Zbl 1383.11094
Liu, Jianya; Sarnak, Peter
38
2015
The horocycle flow at prime times. Zbl 1307.11048
Sarnak, Peter; Ubis, Adrián
22
2015
Notes on thin matrix groups. Zbl 1365.11039
Sarnak, Peter
19
2014
Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions. Zbl 1347.20054
Fuchs, Elena; Meiri, Chen; Sarnak, Peter
12
2014
Disjointness of Moebius from horocycle flows. Zbl 1336.37030
Bourgain, J.; Sarnak, P.; Ziegler, T.
59
2013
Nodal domains of Maass forms. I. Zbl 1328.11044
Ghosh, Amit; Reznikov, Andre; Sarnak, Peter
27
2013
The affine sieve. Zbl 1283.20055
Salehi Golsefidy, Alireza; Sarnak, Peter
16
2013
Real zeros of holomorphic Hecke cusp forms. Zbl 1287.11054
Ghosh, Amit; Sarnak, Peter
20
2012
Möbius randomness and dynamics. Zbl 1473.11147
Sarnak, Peter
4
2012
Recent progress on the quantum unique ergodicity conjecture. Zbl 1317.58036
Sarnak, Peter
1
2012
Generalization of Selberg’s \(\frac {3}{16} \) theorem and affine sieve. Zbl 1276.11081
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
53
2011
Recent progress on the quantum unique ergodicity conjecture. Zbl 1234.58007
Sarnak, Peter
24
2011
Integral Apollonian packings. Zbl 1260.52011
Sarnak, Peter
21
2011
Affine linear sieve, expanders, and sum-product. Zbl 1239.11103
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
64
2010
Prime and almost prime integral points on principal homogeneous spaces. Zbl 1233.11102
Nevo, Amos; Sarnak, Peter
21
2010
Sector estimates for hyperbolic isometries. Zbl 1208.22007
Bourgain, Jean; Kontorovich, Alex; Sarnak, Peter
15
2010
Integral points on quadrics in three variables whose coordinates have few prime factors. Zbl 1230.11045
Liu, Jianya; Sarnak, Peter
14
2010
Linking numbers of modular knots. Zbl 1206.57011
Sarnak, Peter
3
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
13
2009
Strong spectral gaps for compact quotients of products of \(\text{PSL}(2,\mathbb R)\). Zbl 1254.11050
Kelmer, Dubi; Sarnak, Peter
11
2009
The variance of arithmetic measures associated to closed geodesics on the modular surface. Zbl 1231.11057
Luo, Wenzhi; Rudnick, Zeév; Sarnak, Peter
8
2009
Equidistribution and primes. Zbl 1223.11112
Sarnak, Peter
8
2008
Some applications of modular forms. Paperback reprint. Zbl 1141.11023
Sarnak, Peter
2
2008
Some commentary on Atle Selberg’s mathematics. Zbl 1144.01301
Hejhal, D.; Sarnak, P.
2
2008
Reciprocal geodesics. Zbl 1198.11039
Sarnak, Peter
20
2007
Automorphic forms and applications. Papers of the IAS/Park City Mathematics Institute, Park City, UT, USA, July 1–20, 2002. Zbl 1116.11003
2
2007
Minima of Epstein’s zeta function and heights of flat tori. Zbl 1145.11033
Sarnak, Peter; Strömbergsson, Andreas
44
2006
Sieving and expanders. Zbl 1217.11081
Bourgain, Jean; Gamburd, Alex; Sarnak, Peter
33
2006
Notes on the generalized Ramanujan conjectures. Zbl 1146.11031
Sarnak, Peter
42
2005
Selected papers. Vols. I, II. Edited by Peter Sarnak and Andrew Majda. Zbl 1087.01018
Lax, Peter D.
1
2005
What is …an expander? Zbl 1161.05341
Sarnak, Peter
24
2004
Quantum variance for Hecke eigenforms. Zbl 1121.11042
Luo, Wenzhi; Sarnak, Peter
16
2004
Nonvanishing of \(L\)-functions on \(\operatorname{Re}(s)=1\). Zbl 1088.11067
Sarnak, Peter
9
2004
A new method for lower bounds of \(L\)-functions. Zbl 1101.11034
Gelbart, Stephen S.; Lapid, Erez M.; Sarnak, Peter
8
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.
224
2003
Elementary number theory, group theory and Ramanujan graphs. Zbl 1032.11001
Davidoff, Giuliana; Sarnak, Peter; Valette, Alain
89
2003
Spectra of hyperbolic surfaces. Zbl 1045.11033
Sarnak, Peter
39
2003
Mass equidistribution for Hecke eigenforms. Zbl 1044.11022
Luo, Wenzhi; Sarnak, Peter
25
2003
Arithmetic and equidistribution of measures on the sphere. Zbl 1090.11033
Böcherer, Siegfried; Sarnak, Peter; Schulze-Pillot, Rainer
5
2003
Maass cusp forms with integer coefficients. Zbl 1035.11023
Sarnak, Peter
3
2002
Some remarks on Landau-Siegel zeros. Zbl 1008.11033
Sarnak, P.; Zaharescu, A.
2
2002
Estimates for Rankin-Selberg \(L\)-functions and quantum unique ergodicity. Zbl 1006.11022
Sarnak, Peter
61
2001
The distribution of spacings between the fractional parts of \(n^2\alpha\). Zbl 1006.11041
Rudnick, Zeév; Sarnak, Peter; Zaharescu, Alexandru
40
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
16
2001
Low lying zeros of families of \(L\)-functions. Zbl 1012.11041
Iwaniec, Henryk; Luo, Wenzhi; Sarnak, Peter
149
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.
69
2000
The non-vanishing of central values of automorphic \(L\)-functions and Landau-Siegel zeros. Zbl 0992.11037
Iwaniec, Henryk; Sarnak, Peter
68
2000
Selected works of Ilya Piatetski-Shapiro. Edited by James Cogdell, Simon Gindikin and Peter Sarnak. Zbl 0958.01046
Piatetski-Shapiro, Ilya
1
2000
Kloosterman, quadratic forms and modular forms. Zbl 1173.11341
Sarnak, Peter
1
2000
Random matrices, Frobenius eigenvalues, and monodromy. Zbl 0958.11004
Katz, Nicholas M.; Sarnak, Peter
214
1999
Zeroes of zeta functions and symmetry. Zbl 0921.11047
Katz, Nicholas M.; Sarnak, Peter
124
1999
On the generalized Ramanujan conjecture for \(\text{GL}(n)\). Zbl 0965.11023
Luo, Wenzhi; Rudnick, Zeév; Sarnak, Peter
77
1999
Spectra of elements in the group ring of SU(2). Zbl 0916.22009
Gamburd, Alex; Jakobson, Dmitry; Sarnak, Peter
27
1999
Dirichlet \(L\)-functions at the central point. Zbl 0929.11025
Iwaniec, H.; Sarnak, P.
20
1999
Equidistribution of holonomy about closed geodesics. Zbl 0939.22008
Sarnak, Peter; Wakayama, Masato
7
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
43
1998
\(L\)-functions. Zbl 0930.11065
Sarnak, Peter
3
1998
Values at integers of binary quadratic forms. Zbl 0911.11032
Sarnak, Peter
16
1997
Extremal geometries. Zbl 0873.58069
Sarnak, Peter
8
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
2
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
177
1996
On Selberg’s eigenvalue conjecture. Zbl 0844.11038
Luo, W.; Rudnick, Z.; Sarnak, P.
82
1995
\(L^ \infty\) norms of eigenfunctions of arithmetic surfaces. Zbl 0833.11019
Iwaniec, H.; Sarnak, P.
72
1995
Arithmetic quantum chaos. Zbl 0831.58045
Sarnak, Peter
56
1995
Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\). Zbl 0852.11024
Luo, Wenzhi; Sarnak, Peter
53
1995
Selberg’s eigenvalue conjecture. Zbl 1042.11517
Sarnak, Peter
20
1995
Some hypersurfaces in \(\mathbb{P}^ 4\) and the Hasse-principle. Zbl 0857.14013
Sarnak, Peter; Wang, Lan
6
1995
The behaviour of eigenstates of arithmetic hyperbolic manifolds. Zbl 0836.58043
Rudnick, Zeév; Sarnak, Peter
103
1994
Chebyshev’s bias. Zbl 0823.11050
Rubinstein, Michael; Sarnak, Peter
64
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.
60
1994
Integrals of products of eigenfunctions. Zbl 0833.11020
Sarnak, Peter
31
1994
Number variance for arithmetic hyperbolic surfaces. Zbl 0797.58069
Luo, W.; Sarnak, P.
21
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
19
1994
The \(n\)-level correlations of zeros of the zeta function. Zbl 0837.11047
Rudnick, Zeév; Sarnak, Peter
11
1994
Cusp forms for character varieties. Zbl 0804.11038
Phillips, R.; Sarnak, P.
7
1994
Density of integer points on affine homogeneous varieties. Zbl 0798.11024
Duke, W.; Rudnick, Z.; Sarnak, P.
113
1993
Heegner points, cycles and Maass forms. Zbl 0787.11016
Katok, Svetlana; Sarnak, Peter
64
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.
22
1992
Ramanujan duals and automorphic spectrum. Zbl 0762.22009
Burger, Marc; Li, J. S.; Sarnak, P.
19
1992
Automorphic spectrum and Fermi’s golden rule. Zbl 0809.30035
Phillips, R.; Sarnak, P.
6
1992
Bounds for multiplicities of automorphic representations. Zbl 0741.22010
Sarnak, Peter; Xue, Xiaoxi
59
1991
Ramanujan duals. II. Zbl 0774.11021
Burger, Marc; Sarnak, P.
39
1991
...and 44 more Documents
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Cited by 2,612 Authors

58 Sarnak, Peter Clive
41 Bourgain, Jean
29 Blomer, Valentin
27 Zaharescu, Alexandru
22 Lu, Guangshi
21 Ye, Yangbo
20 Kontorovich, Alex V.
20 Rudnick, Zeév
19 Jorgenson, Jay Alan
19 Michel, Philippe Gabriel
18 Oh, Hee
17 Smajlović, Lejla
16 Bétermin, Laurent
16 Gamburd, Alexander
16 Miller, Steven J.
16 Shparlinski, Igor E.
16 Young, Matthew P.
15 Gorodnik, Alexander
15 Kowalski, Emmanuel
15 Lubotzky, Alexander
15 Zelditch, Steve
14 Alon, Noga M.
13 Jiang, Yujiao
13 Luo, Wenzhi
13 Templier, Nicolas
12 Kelmer, Dubi
12 Lau, Yuk-Kam
12 Lemańczyk, Mariusz
12 Liu, Jianya
12 Venkatesh, Akshay
12 Wu, Jie
11 Choi, Junesang
11 Keating, Jonathan Peter
11 Liu, Sheng-Chi
11 Petridis, Yiannis N.
11 Phillips, Ralph Saul
10 Balkanova, Ol’ga Germanovna
10 Duke, William Drexel
10 Frolenkov, Dmitriĭ Andreevich
10 Harcos, Gergely
10 Iwaniec, Henryk
10 Khan, Rizwanur
10 Koyama, Shin-ya
10 Lao, Huixue
10 Linial, Nathan
10 Marklof, Jens
10 Pollicott, Mark
10 Risager, Morten S.
10 Sun, Qingfeng
9 Anantharaman, Nalini
9 Deitmar, Anton
9 Einsiedler, Manfred Leopold
9 Jakobson, Dmitry
9 Katz, Nicholas Michael
9 Kim, Henry H.
9 Lapid, Erez Moshe
9 Nelson, Paul D.
9 Nevo, Amos
9 Rivière, Gabriel
9 Shah, Nimish A.
9 Sharp, Richard W.
9 Snaith, Nina Claire
9 Södergren, Anders
9 Soundararajan, Kannan
9 Tang, Hengcai
8 Aistleitner, Christoph
8 Andrade, Julio Cesar
8 Branson, Thomas Patrick
8 Chandee, Vorrapan
8 Conrey, John Brian
8 Gun, Sanoli
8 Imamoḡlu, Özlem
8 Kurlberg, Pär
8 Lindenstrauss, Elon
8 Magee, Michael
8 Terras, Audrey Anne
8 Wigman, Igor
7 Awonusika, Richard Olu
7 Bergeron, Nicolas
7 Brooks, Robert Wolfe
7 Brumley, Farrell
7 Chang, Sun-Yung Alice
7 Cioabă, Sebastian M.
7 Eswarathasan, Suresh
7 Forrester, Peter J.
7 Fouvry, Etienne
7 Friedman, Joshua S.
7 Gillespie, Timothy L.
7 Huang, Bingrong
7 Judge, Christopher M.
7 Kułaga-Przymus, Joanna
7 Lamzouri, Youness
7 Larcher, Gerhard
7 Lazebnik, Felix
7 Milićević, Djordje
7 Miller, Stephen D.
7 Mohammadi, Amir
7 Naud, Frédéric
7 Parlier, Hugo
7 Parzanchevski, Ori
...and 2,512 more Authors
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Cited in 348 Serials

185 Journal of Number Theory
155 Duke Mathematical Journal
102 Communications in Mathematical Physics
75 Proceedings of the American Mathematical Society
74 Advances in Mathematics
74 Transactions of the American Mathematical Society
65 Israel Journal of Mathematics
61 Geometric and Functional Analysis. GAFA
60 Mathematische Zeitschrift
58 Inventiones Mathematicae
50 International Journal of Number Theory
49 Mathematische Annalen
43 Journal of Functional Analysis
42 Bulletin of the American Mathematical Society. New Series
40 Annals of Mathematics. Second Series
36 Journal of the European Mathematical Society (JEMS)
35 Annales de l’Institut Fourier
33 Journal of the American Mathematical Society
33 The Ramanujan Journal
32 Compositio Mathematica
31 Forum Mathematicum
28 Journal of Mathematical Physics
28 Monatshefte für Mathematik
28 Ergodic Theory and Dynamical Systems
27 Experimental Mathematics
27 Comptes Rendus. Mathématique. Académie des Sciences, Paris
24 Combinatorica
22 Mathematics of Computation
22 Journal für die Reine und Angewandte Mathematik
21 Mathematical Proceedings of the Cambridge Philosophical Society
21 Journal de Théorie des Nombres de Bordeaux
20 Acta Arithmetica
20 Geometriae Dedicata
20 Journal of Combinatorial Theory. Series B
19 Discrete Mathematics
18 Journal d’Analyse Mathématique
17 The Journal of Geometric Analysis
17 Science China. Mathematics
16 Functiones et Approximatio. Commentarii Mathematici
16 Mathematika
16 Algebra & Number Theory
15 Linear Algebra and its Applications
15 Research in Number Theory
14 Journal of Mathematical Analysis and Applications
14 The Annals of Probability
14 Journal of Algebra
14 Manuscripta Mathematica
13 Journal of Statistical Physics
13 Letters in Mathematical Physics
13 Acta Mathematica
13 Theoretical Computer Science
13 European Journal of Combinatorics
13 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
13 Finite Fields and their Applications
13 Journal of the Institute of Mathematics of Jussieu
12 Proceedings of the Japan Academy. Series A
12 Annales Henri Poincaré
12 Journal of Modern Dynamics
11 Archiv der Mathematik
11 Forum of Mathematics, Sigma
10 Discrete Applied Mathematics
10 Nagoya Mathematical Journal
10 Discrete & Computational Geometry
10 Random Structures & Algorithms
10 The Electronic Journal of Combinatorics
10 Discrete and Continuous Dynamical Systems
10 Journal of High Energy Physics
9 Lithuanian Mathematical Journal
9 Rocky Mountain Journal of Mathematics
9 Illinois Journal of Mathematics
9 Combinatorics, Probability and Computing
8 Linear and Multilinear Algebra
8 Journal of Geometry and Physics
8 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
8 Publications Mathématiques
8 Journal of Computational and Applied Mathematics
8 Results in Mathematics
8 Probability Theory and Related Fields
8 Acta Mathematica Sinica. English Series
8 Proceedings of the Steklov Institute of Mathematics
8 Frontiers of Mathematics in China
8 Groups, Geometry, and Dynamics
7 Information Processing Letters
7 Applied Mathematics and Computation
7 Journal of Differential Equations
7 Tohoku Mathematical Journal. Second Series
7 Topology and its Applications
7 Chinese Annals of Mathematics. Series B
7 Revista Matemática Iberoamericana
7 Communications in Partial Differential Equations
7 L’Enseignement Mathématique. 2e Série
7 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
7 Computational Complexity
7 Calculus of Variations and Partial Differential Equations
7 Communications in Contemporary Mathematics
7 International Journal of Geometric Methods in Modern Physics
7 Research in the Mathematical Sciences
6 Bulletin of the Australian Mathematical Society
6 Communications on Pure and Applied Mathematics
6 Nonlinearity
...and 248 more Serials
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Cited in 58 Fields

1,686 Number theory (11-XX)
378 Combinatorics (05-XX)
376 Global analysis, analysis on manifolds (58-XX)
321 Dynamical systems and ergodic theory (37-XX)
249 Topological groups, Lie groups (22-XX)
195 Partial differential equations (35-XX)
191 Algebraic geometry (14-XX)
191 Differential geometry (53-XX)
183 Probability theory and stochastic processes (60-XX)
166 Group theory and generalizations (20-XX)
152 Quantum theory (81-XX)
135 Functions of a complex variable (30-XX)
114 Computer science (68-XX)
88 Linear and multilinear algebra; matrix theory (15-XX)
73 Special functions (33-XX)
66 Operator theory (47-XX)
65 Statistical mechanics, structure of matter (82-XX)
63 Manifolds and cell complexes (57-XX)
61 Several complex variables and analytic spaces (32-XX)
60 Measure and integration (28-XX)
52 Functional analysis (46-XX)
51 Convex and discrete geometry (52-XX)
51 Information and communication theory, circuits (94-XX)
43 Abstract harmonic analysis (43-XX)
36 Harmonic analysis on Euclidean spaces (42-XX)
30 Ordinary differential equations (34-XX)
24 Geometry (51-XX)
23 Approximations and expansions (41-XX)
21 Numerical analysis (65-XX)
19 Relativity and gravitational theory (83-XX)
18 Operations research, mathematical programming (90-XX)
15 Potential theory (31-XX)
13 Real functions (26-XX)
13 Calculus of variations and optimal control; optimization (49-XX)
13 Algebraic topology (55-XX)
13 Statistics (62-XX)
12 Nonassociative rings and algebras (17-XX)
10 Mathematical logic and foundations (03-XX)
10 General topology (54-XX)
10 Mechanics of deformable solids (74-XX)
9 Commutative algebra (13-XX)
9 Integral transforms, operational calculus (44-XX)
8 General and overarching topics; collections (00-XX)
8 Mechanics of particles and systems (70-XX)
7 Biology and other natural sciences (92-XX)
6 Difference and functional equations (39-XX)
5 Field theory and polynomials (12-XX)
5 Sequences, series, summability (40-XX)
5 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
4 Order, lattices, ordered algebraic structures (06-XX)
3 History and biography (01-XX)
3 Associative rings and algebras (16-XX)
3 \(K\)-theory (19-XX)
2 Integral equations (45-XX)
2 Fluid mechanics (76-XX)
1 Optics, electromagnetic theory (78-XX)
1 Astronomy and astrophysics (85-XX)
1 Systems theory; control (93-XX)

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