Additive problems with almost prime squares
Number Theory
2023-02-23 v5
Abstract
We show that every sufficiently large integer is a sum of a prime and two almost prime squares, and also a sum of a smooth number and two almost prime squares. The number of such representations is of the expected order of magnitude. We likewise treat representations of shifted primes p-1 as sums of two almost prime squares. The methods involve a combination of analytic, automorphic and algebraic arguments to handle representations by restricted binary quadratic forms with a high degree of uniformity.
Cite
@article{arxiv.2111.01601,
title = {Additive problems with almost prime squares},
author = {Valentin Blomer and Lasse Grimmelt and Junxian Li and Simon L. Rydin Myerson},
journal= {arXiv preprint arXiv:2111.01601},
year = {2023}
}
Comments
50 pages. We would like to thank the referee for a number of helpful suggestions including clarifications to the proof of Lemma 2.2