The Least Number with Prescribed Legendre Symbols

Abstract

In this article we estimate the number of integers up to $X$ which can be represented by a positive-definite, binary integral quadratic form of discriminant which is small relative to $X$. This follows from understanding the vector of signs when computing the Legendre symbol of small integers $n$ at multiple primes.

arXiv commentThis is the second edition of the article. An error from the first edition has been corrected