Publications

[0] Exponential sums and diophantine problems, Ph. D. Thesis, University of Michigan, 1999.

[1] On simultaneous diagonal inequalities, J. London Math. Soc. (2) 60 (1999), 659--676.

[2] The density of rational lines on cubic hypersurfaces, Trans. Amer. Math. Soc. 352 (2000), 5045--5062.

[3] Multiple exponential sums over smooth numbers, J. Reine Angew. Math. 532 (2001), 47--104.

[4] On simultaneous diagonal inequalities II, Mathematika 48 (2001), 191--202.

[5] (with T. D. Wooley) On pairs of diagonal quintic forms, Compositio Math. 131 (2002), 61--96.

[6] Iterative methods for pairs of additive diophantine equations, Number Theory for the Millennium III (Urbana, IL 2000), pp. 107--118, A K Peters, 2002.

[7] Pairs of additive equations of small degree, Acta Arith. 104 (2002), 345--402.

[8] On simultaneous diagonal inequalities III, Quart. J. Math. 53 (2002), 347--363.

[9] (with T. D. Wooley) A quasi-paucity problem, Michigan Math. J. 50 (2002), 461--469.

[10] Irrational linear forms in prime variables, J. Number Theory 97 (2002), 144--156.

[11] Diophantine approximation with primes and powers of two, New York J. Math. 9 (2003), 363--371.

[12] A generalization of Vinogradov's mean value theorem, Proc. London Math. Soc. (3) 91 (2005), 1--32.

[13] (with J. P. Sorenson) Fast bounds on the distribution of smooth numbers, Algorithmic Number Theory (Berlin, 2006), 168--181, Lecture Notes in Comput. Sci. 4076, Springer, 2006.

[14] Asymptotic estimates for rational linear spaces on hypersurfaces, Trans. Amer. Math. Soc. 361 (2009), 2929--2957.

[15] On the Bombieri-Korobov estimate for Weyl sums, Acta Arith. 138 (2009), 363--372. 

[16] (with J. Mc Laughlin) A Hardy-Ramanujan-Rademacher-type formula for (r,s)-regular partitions, Ramanujan J. 28 (2012), 253--271.

[17] Hua-type iteration for multidimensional Weyl sums, Mathematika 58 (2012), 209--224.

[18] (with S. M. Prendiville and T. D. Wooley) Near-optimal mean value estimates for multidimensional Weyl sums, Geom. Funct. Anal. 23 (2013), 1962--2024.

[19] (with T. D. Wooley) Exceptional sets for Diophantine inequalities, Internat. Math. Res. Notices (in press), 56 pp.

[20] A note on Weyl’s inequality for eighth powers, Rocky Mountain J. Math. (to appear), 7 pp.