Density of the union of positive diagonal binary quadratic forms
Volume 207 / 2023
Acta Arithmetica 207 (2023), 1-17
MSC: Primary 11E16; Secondary 11N56.
DOI: 10.4064/aa210830-24-11
Published online: 9 January 2023
Abstract
Let $X$ be a sufficiently large positive integer. We prove that one may choose a subset $S$ of primes with cardinality $O(\log X)$ such that a positive proportion of integers less than $X$ can be represented by $x^2 + py^2$ for at least one $p \in S$.
