William Duke
- 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
Math Reviews (You must have a subscription to view)
Published Papers (mostly preprint versions) since 2000 (in PDF)
- On elliptic curves and binary quartic forms to appear in IMRN (2021)
- The index of a modular differential operator to appear in Pacific J. Math. dedicated to Raja Varadarajan (2021)
- On a class number formula of Hurwitz with O. Imamoglu and A. Toth, JEMS, 23, Issue 12, (2021), pp. 3995–4008.
- On a theorem of Davenport and Schmidt with N. Andersen, Acta Arithmetica 198 (2021), no. 1, 37–75.
- The Minkowski chain and Diophantine approximation, with N. Andersen, J. Théor. Nombres Bordeaux 32 (2020), no. 2, 503–523.
- Modular invariants for real quadratic fields and Kloosterman sums with N. Andersen, J. Algebra and Number Theory, Vol. 14 (2020), No. 6, 1537–1575
- Riesz means of certain arithmetic functions with H. N. Nguyen, Journal of Number Theory, 210, (2020), 132-141.
- Markov spectra for modular billiards with N. Andersen, Math. Ann. 373 (2019), no. 3-4, 1151–1175.
- Kronecker's first limit formula, revisited with O. Imamoglu and A. Toth..In the Zagier Issue, Res. Math. Sci. 5 (2018), no. 2, Paper No. 20, 21 pp.
- Fourier series of modular graph functions with Eric D'Hoker, J. Number Theory 192 (2018), 1–36.
- Linking numbers and modular cocycles with O. Imamoglu and A. Toth. Duke Math J. 166 (2017), no. 6, 1179-1210.
- Geometric invariants for real quadratic fields with O. Imamoglu and A. Toth. Annals of Math. 184 (2016), no. 3, 949-990.
- Regularized inner products of modular functions with O. Imamoglu and A. Toth, Ramanujan J. 41 (2016), no. 1-3, 13-29.
- Harmonic Maass forms of weight one with Y. Li, Duke Math. J. 164 (2015), no. 1, 39-113.
- The graphic nature of Gaussian periods with S.R. Garcia and B. Lutz, Proc. Amer. Math. Soc. 143 (2015), no. 5, 1849-1863.
- Infinite products of cyclotomic polynomials with Ha Nguyen, Bull. Aust. Math. Soc. 91 (2015), no. 3, 400-411.
- Almost a century of answering the question: What is a mock theta function? Notices Amer. Math. Soc. 61 (2014), no. 11, 1314-1320.
- 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) .
- The subconvexity problem for Artin L–functions, with J. Friedlander and H. Iwaniec, Inventiones Math. 149,489-577 (2002) .
- Bounds for automorphic L–functions. III, with J. Friedlander and H. Iwaniec, Inventiones Math. 148, 221-248 (2001) .
- A problem of Linnik for elliptic curves and mean-value estimates for automorphic representations, with E. Kowalski, Inventiones Math. 139, 1-39 (2000).
Preprints (in PDF)