William Duke

William Duke is an American mathematician and a professor of mathematics at the University of California, Los Angeles (UCLA). He is known for his research in analytic number theory, with a focus on modular forms and the distribution of special points on arithmetic surfaces. Duke has produced influential work on equidistribution theorems and has made significant contributions to our understanding of how certain arithmetic objects are distributed.

All published works

Action	Title	Year	Authors
+	On a method of Hurwitz and its applications	2024	William Duke Özlem Imamoğlu Árpád Tóth
+	Convergence of SARS-CoV-2 spike antibody levels to a population immune setpoint	2024	Eric J. Nilles Kathryn W. Roberts Michael de St. Aubin Helen J. Mayfield Angela Cadavid Restrepo Salomé Garnier Gabriela Abdalla Marie Caroline Etienne William Duke Devan Dumas
+ PDF Chat	On the arithmetic of polynomials over a number field	2024	William Duke
+ PDF Chat	On the analytic theory of isotropic ternary quadratic forms II	2024	William Duke
+ PDF	Trust and COVID-19 vaccine hesitancy in the Dominican Republic: a national cross-sectional household survey, June–October 2021	2024	Salomé Garnier Cecilia Then Michael de St. Aubin Angela Cadavid Restrepo Helen J. Mayfield Devan Dumas William Duke Farah Peña Adam J. Kucharski Ronald Skewes
+ PDF	On the analytic theory of isotropic ternary quadratic forms	2023	William Duke Rainer Schulze‐Pillot
+ PDF Chat	Non-convex geometry of numbers and continued fractions	2023	Nickolas Andersen William Duke Zach Hacking Amy Woodall
+	Higher Rademacher Symbols	2023	William Duke
+ PDF	On sums of fractional parts	2023	William Duke
+ PDF	A Diophantine problem about Kummer surfaces	2022	William Duke
+	Some arithmetic applications of invariant theory	2022	William Duke
+ PDF	Asymptotic distribution of traces of singular moduli	2022	Nickolas Andersen William Duke
+	The index of a modular differential operator	2021	William Duke
+	On Elliptic Curves and Binary Quartic Forms	2021	William Duke
+	On a class number formula of Hurwitz	2021	William Duke Özlem Imamoğlu Árpád Tóth
+	Non-convex geometry of numbers and continued fractions	2021	Nickolas Andersen William Duke Zach Hacking Amy Woodall
+ PDF Chat	On a theorem of Davenport and Schmidt	2020	Nickolas Andersen William Duke
+	Asymptotic distribution of traces of singular moduli.	2020	Nickolas Andersen William Duke
+ PDF	The Minkowski chain and Diophantine approximation	2020	Nickolas Andersen William Duke
+ PDF Chat	Modular invariants for real quadratic fields and Kloosterman sums	2020	Nickolas Andersen William Duke
+ PDF	Riesz means of certain arithmetic functions	2019	William Duke Ha Nam Nguyen
+	The Minkowski chain and Diophantine approximation	2019	Nickolas Andersen William Duke
+	On a theorem of Davenport and Schmidt	2019	Nickolas Andersen William Duke
+	The Minkowski chain and Diophantine approximation	2019	Nickolas Andersen William Duke
+	On a theorem of Davenport and Schmidt	2019	Nickolas Andersen William Duke
+ PDF Chat	Markov spectra for modular billiards	2018	Nickolas Andersen William Duke
+ PDF	Fourier series of modular graph functions	2018	Eric D’Hoker William Duke
+	Kronecker’s first limit formula, revisited	2018	William Duke Özlem Imamoğlu Árpád Tóth
+	Markov spectra for modular billiards	2018	Nickolas Andersen William Duke
+	Markov spectra for modular billiards	2018	Nickolas Andersen William Duke
+	Fourier series of modular graph functions	2017	Eric D’Hoker William Duke
+ PDF	Modular cocycles and linking numbers	2017	William Duke Özlem Imamoğlu Árpád Tóth
+	Fourier series of modular graph functions	2017	Eric D’Hoker William Duke
+ PDF	Geometric invariants for real quadratic fields	2016	William Duke Özlem Imam'glu Árpád Tóth
+ PDF	INFINITE PRODUCTS OF CYCLOTOMIC POLYNOMIALS	2015	William Duke Ha Nam Nguyen
+	Harmonic Maass forms of weight 1	2015	William Duke Y. Li
+	The graphic nature of Gaussian periods	2015	William Duke Stephan Ramon Garcia Bob Lutz
+	Almost a Century of Answering the Question: What Is a Mock Theta Function?	2014	William Duke
+	Regularized inner products of modular functions	2014	William Duke Özlem Imamoğlu Árpád Tóth
+	Notes for a course given at the Second EU/US Summer School on Automorphic Forms on SINGULAR MODULI AND MODULAR FORMS	2014	William Duke Paul A. Jenkins Yingkun Li
+	ARITHMETIC PROPERTIES OF HARMONIC MODULAR FORMS OF WEIGHT ONE (Automorphic forms and automorphic L-functions)	2013	William Duke
+	The graphic nature of Gaussian periods	2012	William Duke Stephan Ramon Garcia Bob Lutz
+	Erratum to "Corrections to: Weyl Sums for Quadratic Roots"	2012	William Duke John Friedlander H. Iwaniec
+	The graphic nature of Gaussian periods	2012	William Duke Stephan Ramon Garcia Bob Lutz
+ PDF	Weyl Sums for Quadratic Roots	2011	William Duke John Friedlander Henryk Iwaniec
+ PDF	Cycle integrals of the j-function and mock modular forms	2011	William Duke Özlem Imamoğlu Árpád Tóth
+ PDF	Real Quadratic Analogs of Traces of Singular Moduli	2010	William Duke Özlem Imamoğlu Árpád Tóth
+ PDF	Rational period functions and cycle integrals	2010	William Duke Özlem Imamoğlu Árpád Tóth
+ PDF	Integral traces of singular values of weak Maass forms	2008	William Duke Paul A. Jenkins
+	Some entries in Ramanujan's notebooks	2008	William Duke
+ PDF	On the Zeros and Coefficients of Certain Weakly Holomorphic Modular Forms	2008	William Duke Paul A. Jenkins
+	Algebra & Number Theory	2008	William Duke Paul A. Jenkins
+ PDF	The zeros of the Weierstrass $$\wp$$ –function and hypergeometric series	2007	William Duke Özlem Imamoğlu
+	A combinatorial problem related to Mahler's measure	2007	William Duke
+	AN INTRODUCTION TO THE LINNIK PROBLEMS	2007	William Duke
+ PDF	On a formula of Bloch	2007	William Duke Özlem Imamoğlu
+	Analytic number theory : a tribute to Gauss and Dirichlet	2007	William Duke Yuri Tschinkel
+ PDF	Special values of multiple gamma functions	2006	William Duke Özlem Imamoğlu
+	Modular units	2006	William Duke Amanda Folsom
+ PDF	Modular functions and the uniform distribution of CM points	2005	William Duke
+	Quadratic Reciprocity in a Finite Group	2005	William Duke Kimberly Hopkins
+ PDF Chat	Quadratic Reciprocity in a Finite Group	2005	William Duke Kimberly Hopkins
+ PDF	Continued fractions and modular functions	2005	William Duke
+	On ternary quadratic forms	2004	William Duke
+	Number fields with large class group	2004	William Duke
+	Reductions of an elliptic curve and their Tate-Shafarevich groups	2004	Alina Carmen Cojocaru William Duke
+	None	2004	William Duke Özlem Imamoğlu
+ PDF	Almost all reductions modulo p of an elliptic curve have a large exponent	2003	William Duke
+ PDF	None	2003	William Duke
+	None	2003	William Duke
+	Number fields with large class groups	2003	William Duke
+	Rational Points on the Sphere	2003	William Duke
+	Quadratic reciprocity in a finite group	2003	William Duke Kimberly Spears
+	The subconvexity problem for Artin L -functions	2002	William Duke John Friedlander H. Iwaniec
+ PDF	Book Review: Character sums with exponential functions and their applications	2002	William Duke
+ PDF	The Splitting of Primes in Division Fields of Elliptic Curves	2002	William Duke Árpád Tóth
+	Bounds for automorphic L-functions. III	2001	William Duke John Friedlander Henryk Iwaniec
+	The splitting of primes in division fields of elliptic curves	2001	William Duke Árpád Tóth
+ PDF	Erratum to: Bounds for automorphic L–functions. II	2000	William Duke John Friedlander Henryk Iwaniec
+	A problem of Linnik for elliptic curves and mean-value estimates for automorphic representations	2000	William Duke Emmanuel Kowalski
+	Automorphic 𝐿-functions in level aspect	1999	William Duke
+	Properties of a ouadratic fibonacci recurrence	1998	William Duke Stephen J. Greenfield Eugène R. Speer
+	Properties of a Quadratic Fibonacci Recurrence	1998	William Duke Stephen J. Greenfield Eugène R. Speer
+	Siegel modular forms of small weight	1998	William Duke x D . Imamoglu
+	Bounds for arithmetic multiplicities	1998	William Duke
+	Courbes elliptiques sur Q sans nombres premiers exceptionnels	1997	William Duke
+	Bilinear forms with Kloosterman fractions	1997	William Duke John Friedlander Henryk Iwaniec
+	Representations by the Determinant and Mean Values of <i>L</i>-Functions	1997	William Duke John Friedlander Henryk Iwaniec
+ PDF	The distribution of the eigenvalues of Hecke operators	1997	J. Brian Conrey William Duke David W. Farmer
+	The distribution of the eigenvalues of Hecke operators	1996	J. Brian Conrey William Duke David W. Farmer
+	None	1996	William Duke Özlem Imamoğlu
+	The distribution of the eigenvalues of Hecke operators	1996	J. Brian Conrey William Duke David W. Farmer
+	The critical order of vanishing of automorphicL-functions with large level	1995	William Duke
+	Class group L-functions	1995	William Duke John Friedlander Henryk Iwaniec
+	Equidistribution of Roots of a Quadratic Congruence to Prime Moduli	1995	William Duke John Friedlander Henryk Iwaniec
+	A quadratic divisor problem	1994	William Duke John Friedlander Henryk Iwaniec
+	Bounds for automorphicL-functions. II	1994	William Duke John Friedlander Henryk Iwaniec
+	The Dimension of the Space of Cusp Forms of Weight One	1994	William Duke
+	Convolution $L$-series	1994	William Duke Henryk Iwaniec
+	The Dimension of the Space of Cusp Forms of Weight One	1994	William Duke
+	Bounds for automorphicL-functions	1993	William Duke John Friedlander Henryk Iwaniec
+ PDF	Density of integer points on affine homogeneous varieties	1993	William Duke Zeév Rudnick Peter Sarnak
+	Estimating Hecke eigenvalues of Siegel modular forms	1992	William Duke Roger Howe J.-S. Li
+	Estimates for coefficients of L-functions. III	1992	William Duke Henryk Iwaniec
+ PDF	On multiple Salié sums	1992	William Duke
+	Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids	1990	William Duke Rainer Schulze‐Pillot
+	Bilinear forms in the Fourier coefficients of half-integral weight cusp forms and sums over primes	1990	William Duke Henryk Iwaniec
+ PDF	Some problems in multidimensional analytic number theory	1989	William Duke
+	Fourth moments of <i>L</i>‐functions attached to newforms	1988	William Duke
+	Hyperbolic distribution problems and half-integral weight Maass forms	1988	William Duke

Common Coauthors

Coauthor	Papers Together
Nickolas Andersen	14
Özlem Imamoğlu	13
Henryk Iwaniec	13
John Friedlander	12
Árpád Tóth	11
Paul A. Jenkins	4
David W. Farmer	3
J. Brian Conrey	3
Eric D’Hoker	3
Bob Lutz	3
Stephan Ramon Garcia	3
Marie Caroline Etienne	2
Salomé Garnier	2
Amy Woodall	2
Angela Cadavid Restrepo	2
Helen J. Mayfield	2
Eric J. Nilles	2
Devan Dumas	2
Eugène R. Speer	2
Stephen J. Greenfield	2
Farah Peña	2
Michael de St. Aubin	2
Ha Nam Nguyen	2
H. Iwaniec	2
Kimberly Hopkins	2
Adam J. Kucharski	2
Rainer Schulze‐Pillot	2
Zach Hacking	2
Colleen L. Lau	2
x D . Imamoglu	1
Petr Jarolı́m	1
Gabriela Abdalla	1
Amanda Folsom	1
Yingkun Li	1
Timothy Oasan	1
Kathryn W. Roberts	1
Emily Zielinski Gutiérrez	1
Yuri Tschinkel	1
Lucia de la Cruz	1
Isaac Miguel Sánchez	1
Roger Howe	1
Margaret Baldwin	1
Kimberly Spears	1
Cecilia Then	1
Ronald Skewes	1
Kristy O. Murray	1
Beatriz López	1
Y. Li	1
Emmanuel Kowalski	1
J.-S. Li	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF	Cycle integrals of the j-function and mock modular forms	2011	William Duke Özlem Imamoğlu Árpád Tóth	14
+	Fourier coefficients of modular forms of half-integral weight	1987	Henryk Iwaniec	13
+	Hyperbolic distribution problems and half-integral weight Maass forms	1988	William Duke	13
+	Kloosterman sums and Fourier coefficients of cusp forms	1982	Jean-Marc Deshouillérs Henryk Iwaniec	12
+	On Modular Forms of Half Integral Weight	1973	Goro Shimura	11
+	Bounds for automorphicL-functions	1993	William Duke John Friedlander Henryk Iwaniec	10
+	Traces of singular moduli	2002	Don Zagier	9
+ PDF	Modular functions and the uniform distribution of CM points	2005	William Duke	9
+	Fourier coefficients of modular forms of half-integral weight	1985	Winfried Kohnen	9
+ PDF	The Selberg Trace Formula for PSL(2,ℝ)	1983	Dennis A. Hejhal	8
+	Analytic Number Theory	2004	Henryk Iwaniec Emmanuel Kowalski	7
+	Introduction to the Arithmetic Theory of Automorphic Functions	1972	Marvin Tretkoff Goro Shimura	7
+	Lectures on advanced analytic number theory	1961	Carl Ludwig Siegel S. Raghavan	7
+ PDF	A mean-value theorem for character sums.	1992	John Friedlander Henryk Iwaniec	6
+	Heegner points, cycles and Maass forms	1993	Svetlana Katok Peter Sarnak	6
+ PDF	On the evaluation of Salié sums	2004	Árpád Tóth	6
+	On Character Sums and <i>L</i> -Series. II	1963	D. A. Burgess	6
+	Bounds for automorphic L-functions. III	2001	William Duke John Friedlander Henryk Iwaniec	6
+ PDF	Primes of the form x2 + ny2: Fermat, class field theory, and complex multiplication	1990	David A. Cox	6
+	Values ofL-series of modular forms at the center of the critical strip	1981	Winfried Kohnen Don Zagier	6
+ PDF	A class of nonanalytic automorphic functions	1973	Douglas Niebur	6
+	Hilbert class polynomials and traces of singular moduli	2005	Jan Hendrik Bruinier Paul A. Jenkins Ken Ono	6
+	Harmonic Analysis and Discontinuous Groups in Weakly Symmetric Riemannian Spaces With Applications to Dirichlet Series	1956	Atle Selberg	6
+	On two geometric theta lifts	2004	Jan Hendrik Bruinier Jens Funke	6
+	Some Applications of Modular Forms	1990	Peter Sarnak	6
+ PDF	On the Zeros and Coefficients of Certain Weakly Holomorphic Modular Forms	2008	William Duke Paul A. Jenkins	6
+ PDF	Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus	1976	Friedrich Hirzebruch Don Zagier	5
+	Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. II	1967	Walter Roelcke	5
+	Kloosterman sums and traces of singular moduli	2005	Paul M. Jenkins	5
+	Table of Integrals, Series, and Products	1980		5
+	La conjecture de Weil. I	1974	Pierre Deligne	5
+ PDF	Rational period functions and cycle integrals	2010	William Duke Özlem Imamoğlu Árpád Tóth	5
+	Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids	1990	William Duke Rainer Schulze‐Pillot	5
+ PDF	Weyl Sums for Quadratic Roots	2011	William Duke John Friedlander Henryk Iwaniec	5
+	Topics in Classical Automorphic Forms	1997	Henryk Iwaniec	5
+	Multiplicative Number Theory	1980	H. Davenport	5
+	Fourier coefficients of the resolvent for a Fuchsian group.	1977	John D. Fay	5
+ PDF Chat	Automorphic forms with singularities on Grassmannians	1998	Richard E. Borcherds	5
+	A generalized Kohnen-Zagier formula for Maass forms	2010	Ehud Moshe Baruch Zhengyu Mao	4
+ PDF	Some new results on the Eichler cohomology of automorphic forms	1974	Marvin I. Knopp	4
+ PDF Chat	The Cubic Moment of Central Values of Automorphic L-Functions	2000	J. Brian Conrey Henryk Iwaniec	4
+	The Theory of the Riemann Zeta-Function	1987	E. C. Titchmarsh D. R. Heath‐Brown	4
+	The exponents of the groups of points on the reductions of an elliptic curve	1991	René Schoof	4
+	Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques	1971	Jean-Pierre Serre	4
+	Class group L-functions	1995	William Duke John Friedlander Henryk Iwaniec	4
+ PDF	Grenzkreisgruppen und kettenbruchartige Algorithmen	1965	M. Eichler	4
+	Rational period functions of the modular group	1978	M. I. Knopp	4
+ PDF	The Arithmetic of Elliptic Curves	1986	Joseph H. Silverman	4
+ PDF	Sur les formes quadratiques binaires ind�finies	1880	A. Markoff	4
+	Automorphic forms onO s +2,2(R) and infinite products	1995	Richard E. Borcherds	4