- Professor of Mathematics, UCLA
- Mailing address: UCLA Mathematics Department Box 951555, Los Angeles, CA 90095-1555
- Office: 6119 Math Sciences Building, UCLA
- Phone: 310-825-1652
- email: wdduke at ucla dot edu

Current Courses

- Singular Moduli and Modular Forms with P. Jenkins and Y. Li, Bristol July 2014

- Almost a century of answering the question: What is a mock theta function? to appear in the Notices of the AMS
- Regularized inner products of modular functions with O. Imamoglu and A. Toth, to appear in Ramanujan J.
- Harmonic Maass forms of weight one with Y. Li, to appear in Duke Math. J.
- The graphic nature of Gaussian periods with S.R. Garcia and B. Lutz, to appear PAMS

- Weyl sums for quadratic roots with J. Friedlander and H. Iwaniec , Int Math Res Notices (2012) Vol. 2012 2493-2549
- Cycle integrals of the j-function and mock modular forms with O. Imamoglu and A. Toth, Ann. of Math. (2) 173 (2011), no. 2, 947-981.
- Real quadratic analogues of traces of singular invariants with O. Imamoglu and A. Toth , Int. Math. Res. Not. IMRN 2011, no. 13, 3082-3094
- Rational period functions and cycle integrals with O. Imamoglu and A. Toth , Abh. Math. Semin. Univ. Hambg. 80 (2010), no. 2, 255-264
- Integral traces of singular values of weak Maass forms with P. Jenkins, Algebra and Number Theory, 2 (2008), 573-593.
- The zeros of the Weierstrass P--function and hypergeometric series, with O. Imamoglu,Math. Ann. 340 (2008), no. 4, 897--905.
- Some entries in Ramanujan's notebooks, Proc. Cambridge Phil. Soc. 144, 255 (2008)
- On the zeros and coefficients of certain weakly holomorphic modular forms with P. Jenkins, Pure Appl. Math. Q. 4 (2008), no.~4, 1327--1340.
- A combinatorial problem related to Mahler's measure Bull. Lond. Math. Soc. 39 (2007), no. 5, 741--748.
- On a formula of Bloch, with O. Imamoglu, the Deshouillers Birthday Volume Funct. Approx. Comment. Math. 37 (2007) , part 1, 109--117.
- An introduction to the Linnik problems, in Equidistribution in Number Theory, an Introduction, Springer, (2007), 197-216.
- Special values of multiple gamma functions, with O. Imamoglu, J. Théorie des Nombres Bordeaux 18 (2006), 113--123.
- Modular functions and the uniform distribution of CM points, Math. Ann. 334 (2006), 241--252
- Continued fractions and modular functions , Bull. Amer. Math. Soc. (N.S.) 42 (2005), 137--162
- Quadratic reciprocity in a finite group, with K. Hopkins, Amer. Math. Monthly 112 (2005), no. 3, 251--256.
- On ternary quadratic forms , J. Number Theory 110 (2005), no. 1, 37--43.
- Lattice points in cones and Dirichlet series, with O. Imamoglu, IMRN 53 (2004)
- Number fields with large class groups, in Number Theory, CNTA VII, CRM Proceedings, 2004
- Reductions of an elliptic curve and their Tate-Shafarevich groups , with A. Cojocaru, Math. Annalen 329, 513-534 (2004)
- Extreme values of Artin L-functions and class numbers , Compositio Math. 136, 103-115 (2003)
- Almost all reductions of an elliptic curve have a large exponent, Comptes Rendus. 337/11, 689-692 (2003)
- Rational points on the sphere , The Ramanujan Journal 7 , 235-239 (2003)
- The splitting of primes in division fields of elliptic curves , with A. Toth, Experimental Math. 11,555-565 (2002) .

- Alina Cojocaru
- Brian Conrey
- John Friedlander
- Kim Hopkins
- Roger Howe
- Ozlem Imamoglu
- Henryk Iwaniec
- Paul Jenkins
- Emmanuel Kowalski
- Jian-Shu Li
- Zeev Rudnick
- Peter Sarnak
- Rainer Schulze-Pillot
- Arpad Toth

- Current
- Former