Fax Number: (801) 422-0504
Research Interests:
- Analytic number theory,including exponential sums, sieve methods, prime number distribution
- Diophantine inequalities
- Metric number theory, including sets of fractional dimension
Prizes and Awards:
- Research prize of the Hardy-Ramanujan society (twice)
Publications:
- Numbers with a large prime factor II. Analytic number theory, Essays in honour of Klaus Roth, (2009), 1-14.
- Numbers in a given set with (or without) a large prime factor, Ramanujan Journal, 20 (2010), 275-295.
- Sums of two relatively prime k-th powers, Functiones et Approximatio, 42(1) (2010), 67-112.
- Zeros of a quadratic form at squarefree points, J. Number Theory, 130 (2010), 2119-2146.
- Weyl’s theorem in the measure theory of numbers, Dependence in Probability, Analysis and Number Theory, (2010), 51-72.
- The distribution of k-free numbers, Acta Math. Hungar., 126 (2010), 181-197.
- Primitive lattice points in planar domains, Acta Arithmetica, 142 (2010), 267-302.
- Sequences that omit a box modulo 1, Advances in Math., 227 (2011), 1757-1771.
- Primes in arithmetic progressions to spaced moduli, Acta Arith. 153(2), 2012, pp. 133-159.