Peter Sarnak

Peter Sarnak is a renowned mathematician best known for his work in number theory, analysis, and related fields. He holds positions at Princeton University and the Institute for Advanced Study. Born in South Africa in 1953, Sarnak completed his Ph.D. at Stanford University under the supervision of Paul Cohen. His research includes fundamental contributions to automorphic forms, L-functions, and spectral theory on manifolds. He has received numerous honors, including the Wolf Prize in Mathematics and membership in the National Academy of Sciences. Sarnak’s work has had extensive influence on the development of both analytic and algebraic aspects of number theory.

All published works

Action	Title	Year	Authors
+ PDF Chat	A universal lower bound for certain quadratic integrals of automorphic L–functions	2024	Laurent Clozel Peter Sarnak
+ PDF	Convergence to the Plancherel measure of Hecke eigenvalues	2024	Peter Sarnak Nina Zubrilina
+ PDF Chat	Bounded Cutoff Window for the Non-backtracking Random Walk on Ramanujan Graphs	2023	Evita Nestoridi Peter Sarnak
+ PDF Chat	Integral points on Markoff type cubic surfaces	2022	Amit Ghosh Peter Sarnak
+ PDF	Commutators in $SL_2$ and Markoff surfaces I	2022	Amit Ghosh Chen Meiri Peter Sarnak
+	A universal lower bound for certain quadratic integrals of automorphic L-functions	2022	Laurent Clozel Peter Sarnak
+	Convergence to the Plancherel measure of Hecke Eigenvalues	2022	Peter Sarnak Nina Zubrilina
+	Commutators in $\mathrm{SL}_2$ and Markoff surfaces I	2021	Amit Ghosh Chen Meiri Peter Sarnak
+	Gap sets for the spectra of cubic graphs	2021	Alicia J. Kollár Peter Sarnak
+ PDF	An appreciation of Jean Bourgain’s work	2021	Peter Sarnak
+	Bounded cutoff window for the non-backtracking random walk on Ramanujan Graphs	2021	Evita Nestoridi Peter Sarnak
+ PDF	Stable polynomials and crystalline measures	2020	Pavel Kurasov Peter Sarnak
+	Gap Sets for the Spectra of Cubic Graphs	2020	Alicia J. Kollár Peter Sarnak
+	Gap Sets for the Spectra of Cubic Graphs	2020	Alicia J. Kollár Peter Sarnak
+ PDF Chat	Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands, and Implementations in Circuit Quantum Electrodynamics	2019	Alicia J. Kollár Mattias Fitzpatrick Peter Sarnak Andrew Houck
+	The Quantum variance of the Modular Surface	2019	Peter Sarnak Peng Zhao
+ PDF	Topologies of Nodal Sets of Random Band‐Limited Functions	2018	Peter Sarnak Igor Wigman
+ PDF Chat	Topology and Nesting of the Zero Set Components of Monochromatic Random Waves	2018	Yaiza Canzani Peter Sarnak
+ PDF	Book Review: Prime numbers and the Riemann hypothesis	2018	Peter Sarnak
+	Spatial statistics for lattice points on the sphere I: Individual results	2017	Jean Bourgain Zeév Rudnick Peter Sarnak
+	Super-Golden-Gates for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>P</mml:mi><mml:mi>U</mml:mi><mml:mrow><mml:mo stretchy="true">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="true">)</mml:mo></mml:mrow></mml:math>	2017	Ori Parzanchevski Peter Sarnak
+ PDF Chat	Nodal domains of Maass forms, II	2017	Amit Ghosh André Reznikov Peter Sarnak
+	Topology and nesting of the zero set components of monochromatic random waves	2017	Yaiza Canzani Peter Sarnak
+	Topology and nesting of the zero set components of monochromatic random waves	2016	Yaiza Canzani Peter Sarnak
+	Spatial statistics for lattice points on the sphere I: Individual results	2016	Jean Bourgain Zeév Rudnick Peter Sarnak
+	Markoff triples and strong approximation	2016	Jean Bourgain Alexander Gamburd Peter Sarnak
+ PDF	Local Statistics of Lattice Points on the Sphere	2016	Jean Bourgain Peter Sarnak Zeév Rudnick
+ PDF Chat	Families of L-Functions and Their Symmetry	2016	Peter Sarnak Sug Woo Shin Nicolas Templier
+	Markoff Surfaces and Strong Approximation: 1	2016	Jean Bourgain Alexander Gamburd Peter Sarnak
+ PDF	Topologies of nodal sets of random band limited functions	2016	Peter Sarnak Igor Wigman
+	Spatial statistics for lattice points on the sphere I: Individual results	2016	Jean Bourgain Zeév Rudnick Peter Sarnak
+	Topologies of nodal sets of random band limited functions.	2015	Peter Sarnak Igor Wigman
+	Markoff Triples and Strong Approximation	2015	Jean Bourgain Alex Gamburd Peter Sarnak
+ PDF Chat	The Möbius function and distal flows	2015	Jianya Liu Peter Sarnak
+	Topologies of nodal sets of random band limited functions	2015	Peter Sarnak Igor Wigman
+	Markoff Triples and Strong Approximation	2015	Jean Bourgain Alex Gamburd Peter Sarnak
+ PDF	Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions	2014	Elena Fuchs Chen Meiri Peter Sarnak
+	The horocycle flow at prime times	2014	Peter Sarnak Adrián Ubis
+	The Mobius disjointness conjecture for distal flows	2014	Jianya Liu Peter Sarnak
+	On the topology of the zero sets of monochromatic random waves	2014	Yaiza Canzani Peter Sarnak
+	Families of L-functions and their Symmetry	2014	Peter Sarnak Sug-Woo Shin Nicolas Templier
+ PDF Chat	Nodal Domains of Maass Forms I	2013	Amit Ghosh André Reznikov Peter Sarnak
+	Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions	2013	Elena Fuchs Chen Meiri Peter Sarnak
+ PDF	The affine sieve	2013	Alireza Salehi Golsefidy Peter Sarnak
+	The Quantum Variance of the Modular Surface	2013	Peter Sarnak Peng Zhao Appendix by Michael Woodbury
+	Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions	2013	Elena Fuchs Chen Meiri Peter Sarnak
+	Topologies of nodal sets of random band limited functions	2013	Peter Sarnak Igor Wigman
+	Notes on Thin Matrix Groups	2012	Peter Sarnak
+	Disjointness of Moebius from Horocycle Flows	2012	Jean Bourgain Peter Sarnak Tamar Ziegler
+ PDF	Real zeros of holomorphic Hecke cusp forms	2012	Amit Ghosh Peter Sarnak
+	Randomness in Number Theory	2012	Peter Sarnak
+	Notes on Thin Matrix Groups	2012	Peter Sarnak
+	Local statistics of lattice points on the sphere	2012	Jean Bourgain Peter Sarnak Zeév Rudnick
+	Affine Sieve	2011	Alireza Salehi Golsefidy Peter Sarnak
+	Real zeros of holomorphic Hecke cusp forms	2011	Amit Ghosh Peter Sarnak
+ PDF	Recent progress on the quantum unique ergodicity conjecture	2011	Peter Sarnak
+ PDF	Integral Apollonian Packings	2011	Peter Sarnak
+	The horocycle flow at prime times	2011	Peter Sarnak Adrián Ubis
+	Mobius Randomness and Dynamics	2011	Peter Sarnak
+ PDF	Generalization of Selberg’s $ \frac{3}{{16}} $ theorem and affine sieve	2011	Jean Bourgain Alex Gamburd Peter Sarnak
+	Affine Sieve	2011	Alireza Salehi Golsefidy Peter Sarnak
+	Distjointness of Mobius from horocycle flows	2011	Jean Bourgain Peter Sarnak Tamar Ziegler
+ PDF Chat	Sector Estimates for Hyperbolic Isometries	2010	Jean Bourgain Alex Kontorovich Peter Sarnak
+	Integral points on quadrics in three variables whose coordinates have few prime factors	2010	Jianya Liu Peter Sarnak
+ PDF	The Grand Riemann Hypothesis	2010	Peter Sarnak
+	Sector estimates for hyperbolic isometries	2010	Jean Bourgain Alex Kontorovich Peter Sarnak
+	Linking Numbers of Modular Knots	2010	Peter Sarnak
+ PDF	Prime and almost prime integral points on principal homogeneous spaces	2010	Amos Nevo Peter Sarnak
+	Sector estimates for hyperbolic isometries	2010	Jean Bourgain Alex Kontorovich Peter Sarnak
+ PDF	Affine linear sieve, expanders, and sum-product	2009	Jean Bourgain Alex Gamburd Peter Sarnak
+	A Survey of Peter D. Lax’s Contributions to Mathematics	2009	Helge Holden Peter Sarnak
+ PDF	Strong spectral gaps for compact quotients of products of PSL(2,ℝ)	2009	Dubi Kelmer Peter Sarnak
+	On Linnik and Selberg’s Conjecture About Sums of Kloosterman Sums	2009	Peter Sarnak Jacob Tsimerman
+	Prime and almost prime integral points on principal homogeneous spaces	2009	Amos Nevo Peter Sarnak
+	Generalization of Selberg's 3/16 Theorem and Affine Sieve	2009	Jean Bourgain Alex Gamburd Peter Sarnak
+ PDF Chat	The variance of arithmetic measures associated to closed geodesics on the modular surface	2009	Wenzhi Luo Zeév Rudnick Peter Sarnak
+	LOCALLY CONVEX SPACES OVER NON-ARCHIMEDEAN VALUED FIELDS	2009	Frances Kirwan Peter Sarnak Barry Simon Burt Totaro
+	Strong spectral gaps for compact quotients of products of $\operatorname{PSL}(2,\mathbb {R})$)	2009	Dubi Kelmer Peter Sarnak
+	Equidistribution and primes	2008	Peter Sarnak
+	Spectral gap for products of $\PSL(2,\bbR)$	2008	Dubi Kelmer Peter Sarnak
+	The variance of arithmetic measures associated to closed geodesics on the modular surface	2008	Wenzhi Luo Zeév Rudnick Peter Sarnak
+	Strong Spectral Gaps for Compact Quotients of Products of $\PSL(2,\bbR)$	2008	Dubi Kelmer Peter Sarnak
+	Automorphic Forms and Applications	2007	Peter Sarnak Freydoon Shahidi
+	Sieving and expanders⁎⁎The first author was supported in part by NSF grant DMS-0322370. The second author was supported in part by NSF grant DMS-0111298 and DMS-0501245. The third author was supported in part by Oscar Veblen Fund (IAS) and the NSF.	2006	Jean Bourgain Alex Gamburd Peter Sarnak
+	Minima of Epstein’s Zeta function and heights of flat tori	2006	Peter Sarnak Andreas Strömbergsson
+	Notes on the Generalized Ramanujan Conjectures	2005	Peter Sarnak
+ PDF	Quantum variance for Hecke eigenforms☆	2004	Wei‐Jie Luo Peter Sarnak
+ PDF	A new method for lower bounds of L-functions	2004	Stephen Gelbart Erez Lapid Peter Sarnak
+ PDF Chat	Arithmetic and Equidistribution of Measures on the Sphere	2003	Siegfried Böcherer Peter Sarnak Rainer Schulze‐Pillot
+ PDF	Spectra of hyperbolic surfaces	2003	Peter Sarnak
+	Mass equidistribution for Hecke eigenforms	2003	Wenzhi Luo Peter Sarnak
+	Maass Cusp Forms with Integer Coefficients	2002	Peter Sarnak
+	A Panorama of Number Theory <i>or</i> The View from Baker's Garden	2002	Gisbert Wüstholz Gisbert Wüstholz Gisbert Wüstholz Kunrui Yu Sinnou David Kálmán Győry Yuri Bilu Paula B. Cohen Jürgen Wolfart Peter Sarnak
+	Some remarks on Landau-Siegel zeros	2002	Peter Sarnak Alexandru Zaharescu
+	Quantum unique ergodicity for SL $ _2({\cal O})\!\setminus\! {\bf H}^3 $ and estimates for L-functions	2001	Yiannis N. Petridis Peter Sarnak
+	Estimates for Rankin–Selberg L-Functions and Quantum Unique Ergodicity	2001	Peter Sarnak
+ PDF Chat	The distribution of spacings between the fractional parts of n 2 α	2001	Zeév Rudnick Peter Sarnak Alexandru Zaharescu
+	Elementary Number Theory, Group Theory and Ramanujan Graphs	2001	Giuliana P. Davidoff Peter Sarnak Alain Valette
+	Appendix 4-Regular Graphs with Large Girth	2001	Giuliana P. Davidoff Peter Sarnak Alain Valette
+	Number Theory	2001	Giuliana P. Davidoff Peter Sarnak Alain Valette
+	The word and Riemannian metrics on lattices of semisimple groups . Low lying zeros of families of l-functions . Singular complete integrability	2001	Alexander Lubotsky Shahar Mozes M. S. Raghunathan Henryk Iwaniec Wenzhi Luo Peter Sarnak Laurent Stolovitch
+ PDF Chat	Low lying zeros of families of L-functions	2000	Henryk Iwaniec Wenzhi Luo Peter Sarnak
+	The non-vanishing of central values of automorphic L-functions and Landau-Siegel zeros	2000	Henryk Iwaniec Peter Sarnak
+ PDF	Advances in random matrix theory, zeta functions, and sphere packing	2000	Thomas C. Hales Peter Sarnak M. C. Pugh
+	Selected Works of Ilya Piatetski-Shapiro	2000	Ilya Piatetski-Shapiro James Cogdell Семен Григорьевич Гиндикин Peter Sarnak
+	Perspectives on the Analytic Theory of L-Functions	2000	Henryk Iwaniec Peter Sarnak
+	Kloosterman, quadratic forms and modular forms	2000	Peter Sarnak Peter Sarnak Kloosterman Centennial Celebration
+	Dirichlet L-functions at the central point	1999	Henryk Iwaniec Peter Sarnak
+ PDF	Spectra of elements in the group ring of $\mathrm{SU}(2)$	1999	Alex Gamburd Dmitry Jakobson Peter Sarnak
+	Low lying zeros of families of L-functions	1999	Henryk Iwaniec Wenzhi Luo Peter Sarnak
+ PDF	Zeroes of zeta functions and symmetry	1999	Nicholas Michael Katz Peter Sarnak
+	On the generalized Ramanujan conjecture for 𝐺𝐿(𝑛)	1999	Wenzhi Luo Zeév Rudnick Peter Sarnak
+	Low lying zeros of families of L-functions	1999	Henryk Iwaniec Wenzhi Luo Peter Sarnak
+ PDF	Random Matrices, Frobenius Eigenvalues, and Monodromy	1998	Nicholas M. Katz Peter Sarnak
+	Distribution of low-lying Frobenius eigenvalues in various families	1998	Nicholas Katz Peter Sarnak
+	Large N limits and Fredholm determinants	1998	Nicholas Katz Peter Sarnak
+	Statements of the main results	1998	Nicholas Katz Peter Sarnak
+	GUE discrepancies in various families	1998	Nicholas Katz Peter Sarnak
+	Monodromy of families of curves	1998	Nicholas Katz Peter Sarnak
+	Reduction steps in proving the main theorems	1998	Nicholas Katz Peter Sarnak
+	The Pair Correlation Function of Fractional Parts of Polynomials	1998	Ze x E v Rudnick Peter Sarnak
+	$L$-functions	1998	Peter Sarnak
+	Spectral Theory and L-functions	1997	Peter Sarnak
+	Analytic Number Theory	1997	Yoichi Motohashi Yoichi Motohashi Enrico Bombieri Enrico Bombieri Enrico Bombieri Jörg Brüdern Jan‐Hendrik Evertse John Friedlander Andrew Granville Adolf Hildebrand
+	Spectra and eigenfunctions of laplacians	1997	Peter Sarnak
+	Extremal Riemann Surfaces	1997	J. R. Quine Peter Sarnak
+ PDF	Quantum Chaos, Symmetry, and Zeta functions, I: Quantum Chaos	1997	Peter Sarnak
+	Extremal geometries	1997	Peter Sarnak
+	Extremal Riemann surfaces : from the proceedings of the AMS special session with related papers January 4-5, 1995, San Francisco, California	1997	J. R. Quine Peter Sarnak
+	Zeros of principal L-functions and random matrix theory	1996	Zeév Rudnick Peter Sarnak
+ PDF	Book Review: The Riemann zeta function	1995	Peter Sarnak
+	L ∞ Norms of Eigenfunctions of Arithmetic Surfaces	1995	Henryk Iwaniec Peter Sarnak
+	On Selberg’s Eigenvalue Conjecture	1995	Wenzhi Luo Zeév Rudnick Peter Sarnak
+	Factorization estimates for abelian varieties . Homogénéité de certaines distributions sur les groupes p-adiques . Concentration of measure and isoperimetric inequalities in product spaces . Quantum ergodicity of eigenfunctions on PSL[2](Z)\H[2]	1995	David Masser Gisbert Wüstholz Jean-Loup Waldspurger Michel Talagrand Wenzhi Luo Peter Sarnak
+	On the period matrix of a Riemann surface of large genus (with an Appendix by J.H. Conway and N.J.A. Sloane)	1994	Peter Buser Peter Sarnak
+	Betti numbers of congruence groups	1994	Peter Sarnak Scot Adams Zeév Rudnick
+ PDF	Number variance for arithmetic hyperbolic surfaces	1994	Wenzhi Luo Peter Sarnak
+ PDF	The behaviour of eigenstates of arithmetic hyperbolic manifolds	1994	Zeév Rudnick Peter Sarnak
+	The n-level correlations of zeros of the zeta function	1994	Zeév Rudnick Peter Sarnak
+	Chebyshev's Bias	1994	Michael Rubinstein Peter Sarnak
+	Cusp forms for character varieties	1994	Ralph S. Phillips Peter Sarnak
+	None	1994	Peter Sarnak
+ PDF	Density of integer points on affine homogeneous varieties	1993	William Duke Zeév Rudnick Peter Sarnak
+	Heegner points, cycles and Maass forms	1993	Svetlana Katok Peter Sarnak
+	Relatively prime values of polynomials	1993	James Lee Hafner Peter Sarnak Kevin S. McCurley
+	Automorphic spectrum and Fermi’s Golden Rule	1992	Ralph S. Phillips Peter Sarnak
+ PDF	Ramanujan duals and automorphic spectrum	1992	M. Burger J.-S. Li Peter Sarnak
+	Ramanujan duals and automorphic spectrum	1992	Marc Burger Jianshu Li Peter Sarnak
+ PDF	Perturbation theory for the Laplacian on automorphic functions	1992	Ralph S. Phillips Peter Sarnak
+ PDF	Perturbation Theory for the Laplacian on Automorphic Functions	1992	R. Phillips Peter Sarnak
+	Ramanujan duals and automorphic spectrum	1992	Marc Burger Jianshu Li Peter Sarnak
+	Ramanujan duals II	1991	M. Burger Peter Sarnak
+	Bounds for multiplicities of automorphic representations	1991	Peter Sarnak Xiaoxi Xue
+	The spectrum of fermat curves	1991	Ralph S. Phillips Peter Sarnak
+	Irregular distribution of {nβ}, n=1,2,3,…, quadrature of singular integrands, and curious basic hypergeometric series	1991	K. Driver D. S. Lubinsky G. Petruska Peter Sarnak
+	None	1991	Alex Eskin Zeév Rudnick Peter Sarnak
+ PDF	Poincaré series for SO(n, 1)	1991	James Cogdell Ilya Piatetski-Shapiro Jinshan Li Peter Sarnak
+	Some Applications of Modular Forms	1990	Peter Sarnak
+	Invariant Means on <i>L</i><sup>∞</sup>(<i>S</i><sup> <i>n</i> </sup>)	1990	Peter Sarnak
+	Bounds for Fourier coefficients of 1/2–integral weight	1990	Peter Sarnak
+	Ramanujan Graphs	1990	Peter Sarnak
+	Papers in analysis, number theory and automorphic L-functions	1990	Ilya Piatetski-Shapiro Stephen Gelbart Roger Howe Peter Sarnak
+	Determinants of Laplacians; Heights and Finiteness	1990	Peter Sarnak
+	Diophantine Problems and Linear Groups	1990	Peter Sarnak
+	Moduli Space, Heights and Isospectral Sets of Plane Domains	1989	Brad Osgood R. Phillips Peter Sarnak
+	Special Values of Selberg's Zeta-function**I would like to thank D. Bertrand, R. Phillips and H. Royden for their helpful insights and comments as well as Alvarez-Gaume', Moore, and Vafa, whose paper [1] motivated this paper.	1989	Peter Sarnak
+	Extremals of determinants of Laplacians	1988	Brad Osgood Ralph S. Phillips Peter Sarnak
+	Compact isospectral sets of surfaces	1988	Brad Osgood Ralph S. Phillips Peter Sarnak
+	Ramanujan graphs	1988	Alexander Lubotzky Ralph S. Phillips Peter Sarnak
+	Poincaré series forSO(n, 1)	1987	Jian-Shu Li Ilya Piatetski-Shapiro Peter Sarnak
+	Hecke operators and distributing points on <i>S</i><sup>2</sup>. II	1987	Alexander Lubotzky Ralph S. Phillips Peter Sarnak
+	Geodesics in homology classes	1987	Ralph S. Phillips Peter Sarnak
+ PDF	Determinants of Laplacians	1987	Peter Sarnak
+	Statistical Properties of Eigenvalues of the Hecke Operators	1987	Peter Sarnak
+	Determinants of Laplacians on Surfaces	1987	Peter Sarnak
+	The Selberg Trace Formula and Related Topics	1986	Dennis A. Hejhal Peter Sarnak Audrey Terras
+	Hecke operators and distributing points on the sphere I	1986	Alexander Lubotzky Ralph S. Phillips Peter Sarnak
+	Explicit expanders and the Ramanujan conjectures	1986	Alexander Lubotzky Ralph S. Phillips Peter Sarnak
+	On cusp forms	1986	Peter Sarnak
+	Class numbers of indefinite binary quadratic forms II	1985	Peter Sarnak
+	The weyl theorem and the deformation of discrete groups	1985	Ralph S. Phillips Peter Sarnak
+	On cusp forms for co-finite subgroups ofPSL(2,?)	1985	Ralph S. Phillips Peter Sarnak
+ PDF	Maass cusp forms	1985	Jean-Marc Deshouillérs Henryk Iwaniec Ralph S. Phillips Peter Sarnak
+	Zeros ofL-functions attached to Maass forms	1985	Charles L. Epstein James Lee Hafner Peter Sarnak
+	On the spectrum of the Hecke groups	1985	Ralph S. Phillips Peter Sarnak
+	Fourth moments of grossencharakteren zeta functions	1985	Peter Sarnak
+	On the number of points on certain curves and an uncertainty principle	1985	Peter Sarnak
+ PDF	The determinant of the Eisenstein matrix and Hilbert class fields	1985	Isaac Efrat Peter Sarnak
+ PDF	The laplacian for domains in hyperbolic space and limit sets of Kleinian groups	1985	Ralph S. Phillips Peter Sarnak
+	A new curvature invariant and entropy of geodesic flows	1984	Robert Osserman Peter Sarnak
+	Additive number theory and maass forms	1984	Peter Sarnak
+	Sums of Kloosterman sums	1983	Dorian Goldfeld Peter Sarnak
+ PDF	The arithmetic and geometry of some hyperbolic three manifolds	1983	Peter Sarnak
+ PDF	Entropy estimates for geodesic flows	1982	Peter Sarnak
+	Class numbers of indefinite binary quadratic forms	1982	Peter Sarnak
+	Spectral behavior of quasi periodic potentials	1982	Peter Sarnak
+	Asymptotic behavior of periodic orbits of the horocycle flow and eisenstein series	1981	Peter Sarnak
+	Explicit solutions of $\square u = 0$ on the Friedmann-Robertson-Walker space-times	1981	Sergiù Klainerman Peter Sarnak
+	Spectra of singular measures as multipliers on Lp	1980	Peter Sarnak
+	Prime geodesic theorems	1980	Peter Sarnak

Common Coauthors

Coauthor	Papers Together
Jean Bourgain	18
Zeév Rudnick	16
Ralph S. Phillips	16
Wenzhi Luo	11
Henryk Iwaniec	9
Nicholas Katz	7
Amit Ghosh	7
Alex Gamburd	7
Igor Wigman	5
Chen Meiri	5
Alexander Lubotzky	4
Dubi Kelmer	4
Yaiza Canzani	4
Ilya Piatetski-Shapiro	4
Alicia J. Kollár	4
Elena Fuchs	3
Alain Valette	3
Brad Osgood	3
Alireza Salehi Golsefidy	3
Alex Kontorovich	3
Jianya Liu	3
Giuliana P. Davidoff	3
Jianshu Li	2
T. N. Shorey	2
M. Burger	2
Adrián Ubis	2
J. R. Quine	2
André Reznikov	2
Marc Burger	2
Jan‐Hendrik Evertse	2
Nina Zubrilina	2
Nicolas Templier	2
Alexander Gamburd	2
Tamar Ziegler	2
Gisbert Wüstholz	2
Enrico Bombieri	2
Laurent Clozel	2
David Masser	2
James Cogdell	2
Alexandru Zaharescu	2
Evita Nestoridi	2
Amos Nevo	2
Stephen Gelbart	2
James Lee Hafner	2
Jacob Tsimerman	1
M. Ram Murty	1
Sug-Woo Shin	1
Yoichi Motohashi	1
Alex Eskin	1
Andrzej Schinzel	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Harmonic Analysis and Discontinuous Groups in Weakly Symmetric Riemannian Spaces With Applications to Dirichlet Series	1956	Atle Selberg	19
+ PDF	The Selberg Trace Formula for PSL(2,ℝ)	1983	Dennis A. Hejhal	19
+	The Asymptotic Distribution of Lattice Points in Euclidean and Non-Euclidean Spaces	1982	Peter D. Lax Ralph S. Phillips	18
+	On the estimation of Fourier coefficients of modular forms	1965	Atle Selberg	17
+	Analytic Number Theory	2004	Henryk Iwaniec Emmanuel Kowalski	15
+	La conjecture de Weil. I	1974	Pierre Deligne	14
+ PDF	Automorphic Forms on GL (2)	1970	H. Jacquet R. P. Langlands	13
+	Rational Quadratic Forms	1982	J. W. S. Cassels	12
+	Coefficients of Maass Forms and the Siegel Zero	1994	Jeffrey Hoffstein Paul Lockhart	12
+	Perspectives on the Analytic Theory of L-Functions	2000	Henryk Iwaniec Peter Sarnak	12
+	The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces	1982	Peter D. Lax Ralph S. Phillips	11
+ PDF	Uniform expansion bounds for Cayley graphs of SL<sub>2</sub>(𝔽<sub>p</sub>)	2008	Jean Bourgain Alex Gamburd	11
+	Bounds for multiplicities of automorphic representations	1991	Peter Sarnak Xiaoxi Xue	11
+	On Some Exponential Sums	1948	André Weil	11
+	Multiplicative Number Theory	1980	H. Davenport	11
+	The Theory of the Riemann Zeta-Function	1987	E. C. Titchmarsh D. R. Heath‐Brown	11
+	Notes on the Generalized Ramanujan Conjectures	2005	Peter Sarnak	11
+	Congruence Properties of Zariski-Dense Subgroups I	1984	Christopher R. Matthews L. N. Vaserstein Boris Weisfeiler	10
+	Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂	2002	Henry Kim	10
+ PDF	Small eigenvalues of the Laplace operator on compact Riemann surfaces	1974	Burton Randol	10
+ PDF	A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$	1978	Stephen Gelbart Hervé Jacquet	10
+ PDF	Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups	2000	A. Borel Nolan R. Wallach	9
+	Hyperbolic distribution problems and half-integral weight Maass forms	1988	William Duke	9
+ PDF Chat	Low lying zeros of families of L-functions	2000	Henryk Iwaniec Wenzhi Luo Peter Sarnak	9
+ PDF	Affine linear sieve, expanders, and sum-product	2009	Jean Bourgain Alex Gamburd Peter Sarnak	9
+	Discrete Subgroups of Semisimple Lie Groups	1991	Gregori Aleksandrovitch Margulis	9
+	Zeros of principal L-functions and random matrix theory	1996	Zeév Rudnick Peter Sarnak	9
+	On cusp forms for co-finite subgroups ofPSL(2,?)	1985	Ralph S. Phillips Peter Sarnak	9
+ PDF Chat	Functorial Products for GL 2 × GL 3 and the Symmetric Cube for GL 2	2002	Henry H. Kim Freydoon Shahidi	8
+ PDF	The behaviour of eigenstates of arithmetic hyperbolic manifolds	1994	Zeév Rudnick Peter Sarnak	8
+	Estimates for Rankin–Selberg L-Functions and Quantum Unique Ergodicity	2001	Peter Sarnak	8
+	Démonstration de la conjecture τ	2003	Laurent Clozel	8
+ PDF	The arithmetic and geometry of some hyperbolic three manifolds	1983	Peter Sarnak	8
+	�ber eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichlet scher Reihen durch Funktionalgleichungen	1949	Hans Maaß	8
+	Ramanujan duals II	1991	M. Burger Peter Sarnak	8
+	Fourier coefficients of modular forms of half-integral weight	1987	Henryk Iwaniec	8
+	Algebraic groups and number theory	1992	В. П. Платонов Andrei S. Rapinchuk	8
+	Representation theory and automorphic functions	1969	М. И. Граев Ilya Piatetski-Shapiro I. M. Gel'fand K. A. Hirsch	8
+	Topics in Classical Automorphic Forms	1997	Henryk Iwaniec	7
+ PDF Chat	On the number of nodal domains of random spherical harmonics	2009	Fëdor Nazarov Mikhail Sodin	7
+	Limit Formulas for Multiplicities in L 2 (Γ\G)	1978	David L. DeGeorge Nolan R. Wallach	7
+	On Modular Forms of Half Integral Weight	1973	Goro Shimura	7
+	On the Holomorphy of Certain Dirichlet Series	1975	Goro Shimura	7
+	Analytic Number Theory	2004	Emmanuel Kowalski Henryk Iwaniec	7
+	Prime geodesic theorems	1980	Peter Sarnak	7
+ PDF	Zeta Functions of Simple Algebras	1972	Roger Godement Hervé Jacquet	7
+	Symmetric random walks on groups	1959	Harry Kesten	7
+ PDF	Pseudo-laplaciens. I	1982	Yves Colin de Verdìère	7
+	On Euler Products and the Classification of Automorphic Representations I	1981	H. Jacquet J. A. Shalika	7
+ PDF	The limit set of a Fuchsian group	1976	S. J. Patterson	7