## 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] *A note on
Weyl’s inequality for eighth powers*, Rocky Mountain J. Math. **44** (2014), 259--268.

[20] (with T. D. Wooley) *Exceptional sets for Diophantine
inequalities*, Internat. Math. Res. Notices
(2014), no. 14, 3919--3974.

[21] (with J. Brandes) *Simultaneous additive
equations: Repeated and differing degrees* (submitted), 28 pp.