Representing an integer as the sum of a prime and the product of two small factors

2020/11/21 by Baker, Roger, Harman, Glyn
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2011.10859

Abstract

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 x¹/2 and ab is less than n^c. This strengthens a result of Heath-Brown, which has the requirement c>3/4. We introduce the idea of 'intersecting two sieves' as a tool in the proof of this result.

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