William Duke

• Professor of Mathematics, UCLA
• Phone: 310-825-1652
• Fax: 310-206-6673
• Mailing address: UCLA Mathematics Department Box 951555, Los Angeles, CA 90095-1555
• Office: 6119 Math Sciences Building, UCLA

Current Courses

• Winter 106 Students: You may see your final exam on Wed April 3 from 1-2 in MS 6119
• 205C Introduction to Analytic Number Theory

Math Reviews (You must have a subscription to view)

• Papers by W. Duke

Preprints (in PDF)

• Weight two weakly harmonic Maass forms with O. Imamoglu and A. Toth
• Mock-modular forms of weight one with Y. Li

Preprint Versions of Some Papers (in PDF)

• 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) .

Collaborators

• 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

Grad Students (PhD Year)

• Current
  • Sungjin Kim
  • Yingkun Li

• Former
  • Jack Buttcane
  • Matt Lane
  • John Leo (2008)
  • Amanda Folsom (2006)
  • Nathan Jones (2005)
  • Ryan Daileda (2004)
  • Arpad Toth (1997)

Links

• The Number Theory Group at UCLA
• UCLA math department home page