# Peter Sarnak

#2,911

Most Influential Person Now

South African mathematician

## Peter Sarnak's AcademicInfluence.com Rankings

Peter Sarnakmathematics Degrees

Mathematics

#127

World Rank

#321

Historical Rank

#53

USA Rank

Complex Analysis

#8

World Rank

#19

Historical Rank

#5

USA Rank

Number Theory

#11

World Rank

#25

Historical Rank

#2

USA Rank

Algebraic Geometry

#45

World Rank

#48

Historical Rank

#12

USA Rank

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Mathematics

## Peter Sarnak's Degrees

- PhD Mathematics Stanford University

## Why Is Peter Sarnak Influential?

(Suggest an Edit or Addition)According to Wikipedia, Peter Clive Sarnak is a South African-born mathematician with dual South-African and American nationalities. Sarnak has been a member of the permanent faculty of the School of Mathematics at the Institute for Advanced Study since 2007. He is also Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Sir Andrew Wiles, and is an editor of the Annals of Mathematics. He is known for his work in analytic number theory. He also sits on the Board of Adjudicators and the selection committee for the Mathematics award, given under the auspices of the Shaw Prize.

## Peter Sarnak's Published Works

### Published Works

- Random matrices, Frobenius eigenvalues, and monodromy (1998) (775)
- Zeros of principal $L$-functions and random matrix theory (1996) (583)
- FUNCTORIALITY FOR THE EXTERIOR SQUARE OF GL4 AND THE SYMMETRIC FOURTH OF GL2 (2003) (510)
- Extremals of determinants of Laplacians (1988) (454)
- Zeroes of zeta functions and symmetry (1999) (425)
- Low lying zeros of families of L-functions (1999) (423)
- The behaviour of eigenstates of arithmetic hyperbolic manifolds (1994) (407)
- Elementary number theory, group theory, and Ramanujan graphs (2003) (343)
- Some Applications of Modular Forms (1990) (330)
- Density of integer points on affine homogeneous varieties (1993) (296)
- Perspectives on the Analytic Theory of L-Functions (2000) (250)
- On Selberg's eigenvalue conjecture (1995) (235)
- Chebyshev's Bias (1994) (234)
- Quantum ergodicity of Eigenfunctions on PSL2(Z)/H2 (1995) (204)
- Hecke operators and distributing points on the sphere I (1986) (197)
- Affine linear sieve, expanders, and sum-product (2010) (189)
- Ramanujan graphs (2017) (188)
- Classical and Multilinear Harmonic Analysis (2011) (177)
- Explicit expanders and the Ramanujan conjectures (1986) (175)
- Compact isospectral sets of surfaces (1988) (169)
- The non-vanishing of central values of automorphic L-functions and Landau-Siegel zeros (2000) (169)
- Bounds for multiplicities of automorphic representations (1991) (169)
- Three Lectures on the Mobius Function Randomness and Dynamics (2010) (168)
- Estimates for Rankin–Selberg L-Functions and Quantum Unique Ergodicity (2001) (164)
- Asymptotic behavior of periodic orbits of the horocycle flow and eisenstein series (1981) (159)
- $L^\infty$ norms of eigenfunctions of arithmetic surfaces (1995) (158)
- The Pair Correlation Function of Fractional Parts of Polynomials (1998) (155)
- Heegner points, cycles and Maass forms (1993) (147)
- Spectra of hyperbolic surfaces (2003) (142)
- On cusp forms for co-finite subgroups ofPSL(2,ℝ) (1985) (138)
- Sums of Kloosterman sums (1983) (132)
- Minima of Epstein’s Zeta function and heights of flat tori (2006) (131)
- Class numbers of indefinite binary quadratic forms II (1982) (129)
- The arithmetic and geometry of some hyperbolic three manifolds (1983) (128)
- Determinants of Laplacians (1987) (123)
- The distribution of spacings between the fractional parts of n2α (2000) (123)
- Generalization of Selberg's 3/16 Theorem and Affine Sieve (2009) (119)
- Hecke operators and distributing points on S2. II (1987) (112)
- Ramanujan duals II (1991) (109)
- Geodesics in homology classes (1987) (107)
- What is . . . An expander (2004) (106)
- Notes on the Generalized Ramanujan Conjectures (2005) (105)
- Statistical Properties of Eigenvalues of the Hecke Operators (1987) (103)
- Integrals of products of eigenfunctions (1994) (100)
- Disjointness of Moebius from Horocycle Flows (2013) (96)
- Mobius Randomness and Dynamics (2011) (93)
- The Möbius function and distal flows (2013) (89)
- Recent progress on the quantum unique ergodicity conjecture (2011) (88)
- Nodal Domains of Maass Forms I (2012) (86)
- Topologies of Nodal Sets of Random Band‐Limited Functions (2013) (82)
- Dirichlet L-functions at the central point (1999) (79)
- Spectra of elements in the group ring of SU(2) (1999) (77)
- Notes on Thin Matrix Groups (2012) (75)
- Quantum variance for Hecke eigenforms (2004) (67)
- Number variance for arithmetic hyperbolic surfaces (1994) (66)
- Diophantine Problems and Linear Groups (1990) (65)
- Ramanujan duals and automorphic spectrum (1992) (65)
- Moduli space, heights and isospectral sets of plane domains* (1989) (64)
- Prime Geodesic Theorems (1980) (61)
- The horocycle flow at prime times (2011) (59)
- Sector Estimates for Hyperbolic Isometries (2010) (58)
- Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands, and Implementations in Circuit Quantum Electrodynamics (2019) (58)
- Families of L -Functions and Their Symmetry (2014) (57)
- Integral Apollonian Packings (2011) (55)
- Additive number theory and maass forms (1984) (54)
- Determinants of Laplacians; Heights and Finiteness (1990) (52)
- The weyl theorem and the deformation of discrete groups (1985) (50)
- Perturbation theory for the Laplacian on automorphic functions (1992) (50)
- The laplacian for domains in hyperbolic space and limit sets of Kleinian groups (1985) (49)
- Sieving and expanders (2006) (49)
- Spectral behavior of quasi periodic potentials (1982) (49)
- Real zeros of holomorphic Hecke cusp forms (2011) (48)
- Prime and almost prime integral points on principal homogeneous spaces (2009) (47)
- Generalization of Selberg’s $$ \frac{3}{{16}} $$ theorem and affine sieve (2011) (47)
- Betti numbers of congruence groups (1994) (44)
- Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions (2013) (42)
- The affine sieve (2011) (40)
- A new curvature invariant and entropy of geodesic flows (1984) (40)
- Super-Golden-Gates for PU(2) (2017) (40)
- Markoff Triples and Strong Approximation (2015) (40)
- Fourth moments of grossencharakteren zeta functions (1985) (39)
- Distjointness of Mobius from horocycle flows (2011) (39)
- Local Statistics of Lattice Points on the Sphere (2012) (36)
- The n-level correlations of zeros of the zeta function (1994) (35)
- On Linnik and Selberg’s Conjecture About Sums of Kloosterman Sums (2009) (35)
- The spectrum of fermat curves (1991) (35)
- Integral points on quadrics in three variables whose coordinates have few prime factors (2010) (33)
- Topology and Nesting of the Zero Set Components of Monochromatic Random Waves (2016) (33)
- Equidistribution of holonomy about closed geodesics (1999) (31)
- Zeros ofL-functions attached to Maass forms (1985) (30)
- A new method for lower bounds of L-functions (2004) (29)
- Some hypersurfaces in P4 and the Hasse-principle (1995) (28)
- A celebration of John F. Nash, Jr. (1996) (28)
- Strong spectral gaps for compact quotients of products of PSL(2,R) (2008) (28)
- A proof of Siegel's weight formula (1991) (27)
- Automorphic forms and applications (2007) (27)
- Maass cusp forms. (1985) (26)
- Mass equidistribution for Hecke eigenforms (2003) (26)
- Cusp forms for character varieties (1994) (26)
- Quantum unique ergodicity for SL 2(O)\ H32(O)∖ and estimates for L-functions (2001) (25)
- The determinant of the Eisenstein matrix and Hilbert class fields (1985) (25)
- Arithmetic and Equidistribution of Measures on the Sphere (2002) (24)
- Spatial statistics for lattice points on the sphere I: Individual results (2016) (22)
- Extremal Riemann Surfaces (1997) (21)
- Quantum Chaos, Symmetry, and Zeta functions, I: Quantum Chaos (1997) (21)
- On the topology of the zero sets of monochromatic random waves (2014) (20)
- Spectra of singular measures as multipliers on Lp (1980) (20)
- Stable polynomials and crystalline measures (2020) (19)
- Automorphic spectrum and Fermi’s Golden Rule (1992) (18)
- Poincaré series forSO(n, 1) (1991) (18)
- The Selberg Trace Formula and Related Topics (1986) (18)
- Compact isospectral sets of plane domains. (1988) (18)
- Quantum unique ergodicity for SL2.O/nH3 and estimates forL-functions (2001) (18)
- Nonvanishing of L-functions on (s) = 1 (17)
- Linking Numbers of Modular Knots (2010) (16)
- Markoff Surfaces and Strong Approximation: 1 (2016) (16)
- Quantum unique ergodicity for SL $ _2({\cal O})\!\setminus\! {\bf H}^3 $ and estimates for L-functions (2001) (16)
- Entropy estimates for geodesic flows (1982) (15)
- The variance of arithmetic measures associated to closed geodesics on the modular surface (2008) (14)
- Equidistribution and primes (2008) (14)
- Poincaré series forSO(n, 1) (1987) (14)
- Integral points on Markoff type cubic surfaces (2017) (14)
- The Quantum Variance of the Modular Surface (2013) (14)
- Gap sets for the spectra of cubic graphs (2020) (14)
- Advances in random matrix theory, zeta functions, and sphere packing. (2000) (14)
- Nodal domains of Maass forms, II (2015) (13)
- Hecke Operators and Distributing Points on S 2 . I 1 (2006) (13)
- Non-vanishing of periods of automorphic functions (2001) (13)
- On the spectrum of the Hecke groups (1985) (13)
- Recent Progress on QUE (2009) (12)
- Elementary Number Theory, Group Theory, and Ramanujan Graphs: Graph Theory (2003) (12)
- Selected Works of Ilya Piatetski-Shapiro (2000) (11)
- Explicit solutions of $\square u = 0$ on the Friedmann-Robertson-Walker space-times (1981) (11)
- Class Numbers of Indefinite Binary Quadratic Forms * (2003) (10)
- The Mobius disjointness conjecture for distal flows (2014) (10)
- Some remarks on Landau-Siegel zeros (2002) (10)
- Spectra and eigenfunctions of laplacians (1997) (9)
- Kloosterman, quadratic forms and modular forms (2000) (8)
- Quantum Chaos, Symmetry, and Zeta functions, II: Zeta Functions (1997) (8)
- A Panorama in Number Theory or The View from Baker's Garden: Maass Cusp Forms with Integer Coefficients (2002) (8)
- Kloosterman, quadratic forms and modular forms (2000) (8)
- Special Values of Selberg's Zeta-function (1989) (7)
- The Schur lectures (1992) (1995) (7)
- Spectral gap for products of $\PSL(2,\bbR)$ (2008) (6)
- Comments on Robert Langland ’ s Lecture : “ Endoscopy and Beyond ” (2004) (6)
- Randomness in Number Theory (2012) (5)
- Restriction Theorems and Appendix 1 & 2 (4)
- Extremal Riemann surfaces : from the proceedings of the AMS special session with related papers January 4-5, 1995, San Francisco, California (1997) (4)
- ON THE FREY-MAZUR CONJECTURE OVER LOW GENUS CURVES (2013) (3)
- Monodromy of families of curves (1998) (3)
- On the number of points on certain curves and an uncertainty principle (1985) (3)
- Determinants of Laplacians on Surfaces (1987) (3)
- Problems of the Millennium : The Riemann Hypothesis ( 2004 ) by Peter Sarnak (2007) (3)
- Remembering Paul Cohen (1934-2007) (2010) (2)
- Commutators in $SL_2$ and Markoff surfaces I (2021) (2)
- Convergence to the Plancherel measure of Hecke Eigenvalues (2022) (2)
- Some commentary on Atle Selberg’s mathematics (2008) (2)
- Bounded cutoff window for the non-backtracking random walk on Ramanujan Graphs (2021) (1)
- Some applications of modular forms: Introduction (1990) (1)
- A universal lower bound for certain quadratic integrals of automorphic L-functions (2022) (1)
- Derivation of the reflection integral equation of the zeta function by the quaternionic analysis (2015) (1)
- Maryam Mirzakhani: 1977–2017 (2018) (1)
- Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands, and Implementations in Circuit Quantum Electrodynamics (2019) (1)
- N T ] 5 O ct 2 01 1 DISJOINTNESS OF MOBIUS FROM HOROCYCLE FLOWS (2013) (1)
- Special issue on the occasion of Fritz Grunewald’s 60th birthday (2011) (1)
- Remembering Jean Bourgain (1954–2018) (2021) (1)
- Domains in Hyperbolic Space and Limit Sets of Kleinian Groups (1984) (1)
- The Grand Riemann Hypothesis (2010) (1)
- ON THE WORK OF AKSHAY VENKATESH (2019) (0)
- Kloosterman Centennial Celebration Kloosterman , quadratic forms and modular forms (2012) (0)
- In Memory of Marina Ratner 1938–2017 (2019) (0)
- Invariant Means on L∞(Sn ) (1990) (0)
- Compact lsospectral Sets of Surfaces * (2009) (0)
- 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) (0)
- Lectures on Lyapunov Exponents (2014) (0)
- GUE discrepancies in various families (1998) (0)
- Cambridge Studies in Advanced Mathematics 121 Representation Theory of the Symmetric Groups Cambridge Studies in Advanced Mathematics Representation Theory of the Symmetric Groups Central Projection Formulas 22 1.4 Permutation Representations 27 1.4.1 Wielandt's Lemma 27 1.4.2 Symmetric Actions and (2010) (0)
- Coffee Coffee Coffee Coffee Coffee 1100-1200 (2012) (0)
- ISOSPECTRAL MANIFOLDS WITH DIFFERENT LOCAL GEOMETRIES 3 (2001) (0)
- The Selberg trace formula and related topics : proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 22-28, 1984, with support from the National Science Foundation (1999) (0)
- Arithmeticity ( or not ) of Monodromy Peter Sarnak April 23 , 2013 (2013) (0)
- Foreword (2020) (0)
- Schedule of talks (2016) (0)
- On the occasion of Robert Osserman ’ s retirement (1995) (0)
- Bounds for Fourier coefficients of 1/2–integral weight (1990) (0)
- Appendix 4-Regular Graphs with Large Girth (2003) (0)
- Analytic Number Theory: Spectral Theory and L-functions (1997) (0)
- Maass cusp forms ( L function / Teichmfiller space ) (0)
- An appreciation of Jean Bourgain’s work (2021) (0)
- Ratner's Work on Unipotent Flows and Impact (2019) (0)
- Nodal Domains of Maass Forms I (2013) (0)
- Band Engineering for Quantum Simulation in Circuit QED (2019) (0)
- Papers in analysis, number theory and automorphic L-functions (1990) (0)
- SPECTRAL THEORY OF AUTOMORPHIC FORMS LECTURES BY PETER SARNAK, NOTES BY TONY FENG AND GYUJIN OH (2018) (0)
- Book Review: The Riemann zeta function (1995) (0)
- Monodromy of some other families (1998) (0)
- Distribution of low-lying Frobenius eigenvalues in various families (1998) (0)
- Reduction steps in proving the main theorems (1998) (0)
- Some applications of modular forms: Modular Forms (1990) (0)
- Papers in representation theory (1990) (0)
- Some applications of modular forms: Preface (1990) (0)
- Reformulation of the main results (1998) (0)
- 153 Abelian Varieties , Theta Functions and the Fourier Transform (2012) (0)
- MARKOFF TRIPLES AND STRONG APPROXIMATION TRIPLETS DE MARKOFF ET APPROXIMATION FORTE (2016) (0)
- Elementary Number Theory, Group Theory, and Ramanujan Graphs: Bibliography (2003) (0)
- Book Review: Prime numbers and the Riemann hypothesis (2018) (0)
- A Survey of Peter D. Lax’s Contributions to Mathematics (2010) (0)
- Communications in Mathematical Physics: Preface (2004) (0)
- Title : Ergodic Properties of Square-Free Numbers (2012) (0)
- 978-0-521-51918-2-Random Walk : A Modern Introduction (2010) (0)
- RECENT PROGRESS ON THE QUANTUM UNIQUE ERGODICITY (2011) (0)
- The Graphs Xp, q (2003) (0)
- Additive Combinatorics (2006) (0)
- Statements of the main results (1998) (0)
- Large N limits and Fredholm determinants (1998) (0)

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Peter Sarnak is affiliated with the following schools: