Publications

[14] Asymptotic estimates for rational linear spaces on hypersurfaces, Trans. Amer. Math. Soc. (to appear), 29 pp. pdf

[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. pdf

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

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

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

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

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

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

[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. pdf

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

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

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

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

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

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