Density of the union of positive diagonal binary quadratic forms

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 $x^2+p{y}^2$ for at least one of $p\in S$.

13 pages

References in corpus (1)

• Number of integers represented by families of binary forms