4 citations · 5 across the 5 of their papers we have counts for
5 papers · 1 filter
Representing an integer as the sum of a prime and the product of two small factors
Roger Baker, Glyn Harman
Let c > 0.55. Every large n can be written in the form p +ab, where p is prime, a and b are significantly smaller than x^1/2 and ab is less than n^c. This strengthens a result of H…
Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients
Glyn Harman, Igor E. Shparlinski
We show that for any and a sufficiently large cube-free , any reduced residue class modulo can be represented as a product of integers from the interv…
The Duffin-Schaeffer Conjecture with extra divergence II
Victor Beresnevich, Glyn Harman, Alan Haynes +1
This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra dive…
On sums of squares of primes II
Glyn Harman, Angel Kumchev
In this paper we continue our study, begun in part I, of the exceptional set of integers, not restricted by elementary congruence conditions, which cannot be represented as sums of…
On primitive divisors of n^2+b
Graham Everest, Glyn Harman
We study primitive divisors of terms of the sequence P_n=n^2+b, for a fixed integer b which is not a negative square. It seems likely that the number of terms with a primitive divi…