Don Bernard Zagier

Don Bernard Zagier's AcademicInfluence.com Rankings

Don Bernard Zagier

Mathematics

#5328

World Rank

#7504

Historical Rank

Number Theory

#134

World Rank

#176

Historical Rank

Measure Theory

#689

World Rank

#935

Historical Rank

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Mathematics

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Don Bernard Zagier's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Heegner points and derivatives ofL-series (1986) (1059)
The Theory of Jacobi Forms (2013) (854)
Values of Zeta Functions and Their Applications (1994) (755)
The Euler characteristic of the moduli space of curves (1986) (678)
The 1-2-3 of Modular Forms (2008) (454)
Volumes of hyperbolic three-manifolds (1985) (391)
A Generalized Jacobi Theta Function and Quasimodular Forms (1995) (349)
Values ofL-series of modular forms at the center of the critical strip (1981) (338)
The dilogarithm function. (2007) (337)
Elliptic modular forms and their applications. (2008) (326)
Quantum Black Holes, Wall Crossing, and Mock Modular Forms (2012) (320)
Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus (1976) (303)
Modular forms whose fourier coefficients involve zeta-functions of quadratic fields (1977) (274)
Traces of singular moduli (2002) (252)
A Kronecker limit formula for real quadratic fields (1975) (246)
Modular Functions of One Variable III (1973) (221)
Vassiliev invariants and a strange identity related to the Dedekind eta-function (2001) (221)
Heegner points and derivatives ofL-series. II (1987) (214)
Modular forms and differential operators (1994) (211)
The Atiyah-Singer Theorem and Elementary Number Theory (1974) (208)
Periods of modular forms and Jacobi theta functions (1991) (200)
Exact results for perturbative Chern-Simons theory with complex gauge group. (2009) (192)
Quantum modular forms (2010) (189)
Period functions for Maass wave forms. I. (2001) (189)
Ramanujan's mock theta functions and their applications (after Zwegers and Ono-Bringmann) (2009) (186)
AUTOMORPHIC PSEUDODIFFERENTIAL OPERATORS (1997) (164)
Jacobi forms and a certain space of modular forms (1988) (160)
Double Zeta values and modular forms (2006) (160)
Supersingular j-invariants, hypergeometric series, and Atkin's orthogonal polynomials (1998) (159)
Polylogarithms, Dedekind Zeta Functions, and the Algebraic K-Theory of Fields (1991) (154)
The Bloch-Wigner-Ramakrishnan polylogarithm function (1990) (145)
Infinite Grassmannians and Moduli Spaces of G–bundles (1994) (145)
Eisenstein Series and the Riemann Zeta-Function (1981) (138)
Modular forms associated to real quadratic fields (1975) (136)
Higher dimensional dedekind sums (1973) (121)
Integral solutions of Ap`ery-like recurrence equations (1984) (115)
Evaluation of the multiple zeta values (2012) (112)
Newman's short proof of the prime number theorem (1997) (111)
Realizability of a model in infinite statistics (1992) (107)
Multiple zeta values of fixed weight, depth, and height (2001) (99)
Elementary aspects of the Verlinde formula and of the Harder-Narasimhan-Atiyah-Bott formula (1996) (91)
Evaluation of the multiple zeta values $\zeta(2,\dots,2,3,2,\dots,2)$ (2012) (91)
A one-sentence proof that every prime p Ξ1(mod 4) is a sum of two squares (1990) (90)
The Entropy of a Certain Infinitely Convolved Bernoulli Measure (1991) (89)
Jacobi forms and the structure of Donaldson invariants for 4-manifolds with b+ = 1 (1996) (85)
Higher Weil-Petersson volumes of moduli spaces of stablen-pointed curves (1996) (84)
On the number of Markoff numbers below a given bound (1982) (83)
On the conjecture of Birch and Swinnerton-Dyer for an elliptic curve of rank 3 (1985) (83)
Jensen polynomials for the Riemann zeta function and other sequences (2019) (81)
Hyperbolic manifolds and special values of Dedekind zeta-functions (1986) (79)
Large Integral Points on Elliptic Curves (1987) (78)
Note on the Landweber-Stong elliptic genus (1988) (75)
Modular Parametrizations of Elliptic Curves (1985) (74)
PERIODS OF MODULAR FORMS, TRACES OF HECKE OPERATORS, AND MULTIPLE ZETA VALUES (1993) (74)
Densities of Short Uniform Random Walks (2011) (69)
Classical and Elliptic Polylogarithms and Special Values of L-Series (2000) (69)
On the distribution of the number of cycles of elements in symmetric groups (1995) (67)
Special values and functional equations of polylogarithms (1991) (64)
Period functions and the Selberg zeta function for the modular group. (1997) (63)
The First 50 Million Prime Numbers (1977) (63)
Equivariant Pontrjagin Classes and Applications to Orbit Spaces: Applications of the G-signature Theorem to Transformation Groups, Symmetric Products and Number Theory (1972) (61)
Numerical investigations related to the L-series of certain elliptic curves. (1987) (61)
Modular forms and quantum invariants of 3-manifolds. (1999) (61)
Hecke operators and periods of modular forms (1990) (60)
On the singular values of Weber modular functions (1997) (57)
On the cohomology of moduli spaces of rank two vector bundles over curves (1995) (57)
VOLUMES OF HYPERBOLIC 3-MANIFOLDS (1985) (56)
Crossing Probabilities and Modular Forms (2002) (56)
The remarkable dilogarithm (1988) (55)
Modular points, modular curves, modular surfaces and modular forms (1985) (51)
A trace formula for Jacobi forms. (1989) (47)
Quasimodularity and large genus limits of Siegel-Veech constants (2016) (46)
Introduction to modular forms (1992) (43)
Reciprocity formulae for general Dedekind-Rademacher sums. (1995) (43)
Partitions, quasimodular forms, and the Bloch–Okounkov theorem (2016) (43)
Some properties of hypergeometric series associated with mirror symmetry (2007) (43)
Algebraic numbers close to both 0 and 1 (1993) (40)
On the zeros of the Weierstrass ℘-Function (1982) (39)
Square roots of central values of Hecke L-series. (1993) (38)
The dilogarithm function in geometry and number theory (1989) (37)
The Hilbert modular group for the field Q( (1977) (36)
Eisenstein series and the Selberg trace formula. II (1987) (36)
Period Functions for Maass Wave Forms and Cohomology (2015) (36)
Convergence Acceleration of Alternating Series (2000) (36)
Complex Analysis and Algebraic Geometry: Classification of Hilbert Modular Surfaces (1977) (36)
Correction to: Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials (2019) (33)
A proof of the Kac-Wakimoto affine denominator formula for the strange series (2000) (32)
EISENSTEIN SERIES AND THE SELBERG TRACE FORMULA (1987) (31)
Classical Hurwitz numbers and related combinatorics (2016) (31)
ON A CURIOUS PROPERTY OF BELL NUMBERS (2010) (29)
The Hilbert modular group for the field ℚ( $$\sqrt {13} $$ ) (1977) (29)
Arithmetic and Topology of Differential Equations (2016) (29)
Numerical verification of Beilinson's conjecture for K2 of hyperelliptic curves (2004) (29)
Inequalities for the Gini coefficient of composite populations (1983) (28)
A note on an invariant of fintushel and stern (1985) (27)
A Property of Parallelograms Inscribed in Ellipses (2007) (27)
Bernoulli numbers and zeta functions : with an appendix by Don Zagier (2014) (27)
A Sixteenth-order Polylogarithm Ladder (1992) (27)
From quadratic functions to modular functions (1999) (24)
Congruences among generalized Bernoulli numbers (1995) (24)
Sequences of Enumerative Geometry: Congruences and Asymptotics (2006) (23)
Genus-zero and genus-one string amplitudes and special multiple zeta values (2019) (23)
Which primes are sums of two cubes (1995) (21)
Finite projective planes, Fermat curves, and Gaussian periods (2008) (21)
On tau-functions for the KdV hierarchy (2018) (20)
Gromov–Witten invariants of the Riemann sphere (2018) (20)
Finite Size XXZ Spin Chain with Anisotropy Parameter Δ= $$ \frac{1} {2} $$ (2000) (19)
A modified Bernoulli number. (1998) (19)
Modular embeddings of Teichmüller curves (2015) (18)
LETTER TO THE EDITOR: Ground state of the quantum symmetric finite-size XXZ spin chain with anisotropy parameter Delta = ½ (1999) (18)
On the Capacity of Disjointly Shared Networks (1985) (18)
Asymptotics of Nahm sums at roots of unity (2018) (18)
Bloch groups, algebraic $K$-theory, units, and Nahm's Conjecture (2017) (17)
On the existence of a phase transition for an exclusion process on a ring (2001) (16)
Proof of the gamma conjecture for Fano 3-folds of Picard rank 1 (2016) (16)
Higher Kronecker “limit” formulas for real quadratic fields (2012) (16)
A parametric family of quintic polynomials with Galois group D5 (1982) (16)
Knots, perturbative series and quantum modularity (2021) (15)
Appendix. the Mellin Transform and Related Analytic Techniques (15)
Theta Blocks (2019) (15)
Constructions of plane curves with many points (2001) (14)
Lower bounds of heights of points on hypersurfaces (1997) (14)
On the coefficients of the minimal polynomials of Gaussian periods (1993) (13)
The first 50 million prime numbers (1977) (13)
Function Theory Related to the Group PSL2(ℝ) (2013) (13)
Vanishing and non-vanishing theta values (2013) (12)
New points of view on the Selberg zeta function (2002) (12)
A property of L-functions on the real line (1980) (12)
Correction to “The eichler-selberg trace formula on SL2(ℤ)” (1977) (12)
Knots and their related $q$-series (2023) (11)
PERIODS OF MODULAR FORMS ON Γ0(N) AND PRODUCTS OF JACOBI THETA FUNCTIONS (2017) (11)
Masur–Veech volumes of quadratic differentials and their asymptotics (2020) (11)
The Birch-Swinnerton-Dyer Conjecture from a Naive Point of View (1991) (11)
A modular identity arising from mirror symmetry. (1998) (11)
Multiplicative functions with difference tending to zero (2001) (9)
Applications of the representation theory of finite groups (2004) (9)
The Ring of Jacobi Forms (1985) (9)
Modular Forms in One Variable (2019) (8)
The arithmetic and topology of differential equations (2018) (8)
On the critical values of Hecke L-series (1980) (8)
Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials (2020) (7)
Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis (2018) (7)
Quotients Homophones des Groupes Libres Homophonic Quotients of Free Groups (1993) (7)
Explicit Methods in Number Theory (2005) (7)
How often should you beat your kids (1990) (6)
Periods of modular forms on $\Gamma_0(N)$ and products of Jacobi theta functions (2017) (6)
Curious and Exotic Identities for Bernoulli Numbers (2014) (6)
RATIONAL PERIOD FUNCTIONS FOR PSL(2,Z) (2011) (6)
The Pontrjagin class of an orbit space (1972) (6)
Arithmetic properties of the Herglotz function (2020) (6)
Power partitions and a generalized eta transformation property (2022) (5)
Dynamics of geodesics, and Maass cusp forms (2019) (5)
LINES ON THE DWORK QUINTIC PENCIL AND ITS HIGHER DEGREE ANALOGUES (2014) (5)
Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality (2021) (5)
Some questions and observations around the mathematics of Seki Takakazu (2013) (4)
Modular functions of one variable, V-VI : proceedings, international conference, University of Bonn, Sonderforschungsbereich Theoretische Mathematik, July 2-14, 1976 (1977) (4)
Higher-rank zeta functions and SLn-zeta functions for curves (2020) (4)
CONGRUENCES MODULO POWERS OF 2 FOR THE SIGNATURE OF COMPLETE INTERSECTIONS (1980) (4)
A combinatorial refinement of the Kronecker-Hurwitz class number relation (2016) (4)
Higher-rank zeta functions for elliptic curves (2020) (4)
The 1-2-3 of modular forms. Lectures at a summer school in Nordfjordeid, Norway, June 2004. (2008) (4)
On an approximate identity of Ramanujan (1987) (4)
Calabi-Yau Varieties and Mirror Symmetry (4)
New Looks at Old Number Theory (2013) (3)
A Refinement of a Theorem of J. E. Littlewood (2014) (3)
Nu-invariants of extra-twisted connected sums (2020) (3)
Life and Work of Friedrich Hirzebruch (2015) (3)
D-brane masses at special fibres of hypergeometric families of Calabi-Yau threefolds, modular forms, and periods (2022) (3)
Information thermodynamics of financial markets: the Glosten–Milgrom model (2020) (3)
FALTINGS HEIGHTS AND THE DERIVATIVE OF ZAGIER ’ S EISENSTEIN SERIES (2004) (2)
AN EXACT SEQUENCE FOR THE BROADHURST-KREIMER CONJECTURE (2013) (2)
Addendum to: “Large integral points on elliptic curves” [Math. Comp. 48 (1987), no. 177, 425–436; MR0866125 (87k:11062)] (1988) (2)
Relations among invariants of circle actions on three-manifolds (1971) (2)
Elliptische Kurven: Fortschritte und Anwendungen. (Elliptic curves: Progress and applications). (1990) (2)
Expansion of an n-Point Function as a Sum of Commutators (1970) (1)
A Converse to Cauchy's Inequality (1995) (1)
TWO RESULTS IN NUMBER THEORY WITH ELEMENTARY ASPECTS(Algebraic Number Theory : Recent Developments and Their Backgrounds) (1993) (1)
A curious identity that implies Faber's conjecture (2021) (1)
A hyperbolic Kac-Moody Calogero model (2022) (1)
Friedrich Hirzebruch (1927--2012) (2014) (1)
Interpolated Apéry numbers, quasiperiods of modular forms, and motivic gamma functions (2021) (1)
An elementary proof of the Eichler–Selberg trace formula (2017) (1)
Low-Dimensional Topology and Number Theory (2018) (1)
Deligne Products of Line Bundles over Moduli Spaces of Curves (2008) (1)
Dimensional interpolation and the Selberg integral (2019) (1)
The G-signature theorem and some elementary number theory (1972) (0)
Life and Work of Friedrich Hirzebruch (2015) (0)
Mathematisches Forschungsinstitut Oberwolfach Report No . 32 / 2005 Explicit Methods in Number Theory (2005) (0)
APPENDIX: SPECIAL VALUES AND FUNCTIONAL EQUATIONS OF POLYLOGARITHMS (2011) (0)
Annals of Mathematics Period Functions for Maass Wave Forms (2010) (0)
Newman's Short Proof of the Prime (1997) (0)
2 2 M ar 2 01 5 Dyson ’ s Brownian-motion model for random matrix theory-revisited (2015) (0)
Low-dimensional topology and number theory. Abstracts from the workshop held August 15th--August 21st, 2010. (2010) (0)
A passion for mathematics (2011) (0)
Strichartz estimates with broken symmetries (2020) (0)
L-series and the Green's functions of modular curves (1987) (0)
Asymptotics of Nahm sums at roots of unity (2020) (0)
Appendix: On Harder's \\textSl(2,\\bbfR)-\\textSl(3,\\bbfR)-identity (2011) (0)
The equivalence of two sets of relations (2007) (0)
L-classes of symmetric froducts (1972) (0)
Appendix: Polynomials Arising from the Tautological Ring (2000) (0)
SOME PROBLEMS RELATED TO POLYLOGARITHMS (2011) (0)
L-classes of rational homology manifolds (1972) (0)
Hyperbolic 3-manifolds, the Bloch group, and the work of Walter Neumann (2023) (0)
THE CONJECTURE OF BIRCH AND SWINNERTON-DYER (2011) (0)
Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis (2018) (0)
The 1-2-3 of modular forms : Lectures at a summer school in Nordfjordeid , Norway Link to publication (2008) (0)
PERlon FUNCTIONS AND THE SELBERG ZETA FUNCTION FOR TUE MODULAR GROUP (2007) (0)
STABLE PAIRS WITH DESCENDENTS ON LOCAL SURFACES I: THE VERTICAL COMPONENT MARTIJN KOOL AND RICHARD THOMAS (2016) (0)
A Property of Parallelograms Inscribed in Ellipses Author ( s ) : (2010) (0)
Partitions, quasimodular forms, and the Bloch–Okounkov theorem (2015) (0)
ON THE LEFSCHETZ THEOREM FOR THE COMPLEMENT OF A CURVE IN (2017) (0)
Modular Linear Differential Operators and Generalized Rankin-Cohen Brackets (2022) (0)
A G ] 9 M ay 2 01 6 STABLE PAIRS WITH DESCENDENTS ON LOCAL SURFACES (2018) (0)
Rational period functions for \textPSL(2,\Bbb Z). (1993) (0)
Relations with Other Types of Modular Forms (1985) (0)
On tau-functions for the KdV hierarchy (2021) (0)
Correction to: Masur–Veech volumes and intersection theory on moduli spaces of Abelian differentials (2021) (0)
Entering Fritz's orbit (2014) (0)
A Kronecker Limit Formula for (1975) (0)
Problems and solutions : solutions : 6625 (1992) (0)
Explicit methods in number theory. Abstracts from the workshop held July 12th--July 18th, 2009. (2009) (0)
Report 32/2005: Explicit methods in number theory (July 17th -- July 23rd, 2005). (2005) (0)
Vanishing and non-vanishing theta values (2013) (0)
The 1-2-3 of modular forms : Lectures at a summer school in Nordfjordeid , Norway (2008) (0)
S I ] 1 1 O ct 2 00 0 Finite Size XXZ Spin Chain with Anisotropy Parameter ∆ = 1 2 (2022) (0)
A note on Reyes's theorem about triangles (1996) (0)
THE ENTROPY OF A CERTAIN INFINITELY CONVOLVED (2017) (0)
Addendum to "Large integral points on elliptic curves" (1988) (0)
TRACES OF SINGULAR MODULI Don Zagier (2011) (0)

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