4 papers
math.NT2016
Small fractional parts of polynomials
Roger Baker
Using the recent result of Bourgain, Demeter and Guth on Vinogradov's mean value, a number of new results about small fractional parts of polynomials and fractional parts of additi…
math.NT2016
Primes in arithmetic progressions to spaced moduli.III
Roger Baker
We obtain the analog of the Bombieri-Vinogradov theorem for square moduli up to any power of x less than 1/2.
math.NT2015
Clusters of primes with square-free translates
Roger C. Baker, Paul Pollack
Let be a finite set of integers satisfying appropriate local conditions. We show the existence of long clusters of primes in bounded length intervals with s…
math.NT2015
Bounded intervals containing many primes
R. C. Baker, A. J. Irving
By combining a sieve method of Harman with the work of Maynard and Tao we show that