The least number with prescribed Legendre symbols and representation by binary quadratic forms of small discriminant

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Abstract

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

Original languageEnglish (US)
Pages (from-to)3-16
Number of pages14
JournalJournal of Number Theory
Volume179
DOIs
StatePublished - Oct 1 2017

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Binary Quadratic Forms
Legendre
Discriminant
Integer
Quadratic form
Positive definite
Estimate
Binary
Computing

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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title = "The least number with prescribed Legendre symbols and representation by binary quadratic forms of small discriminant",
abstract = "In this article we estimate the number of integers up to X which can be properly represented by a positive-definite, binary, integral quadratic form of small discriminant. This estimate follows from understanding the vector of signs that arises from computing the Legendre symbol of small integers n at multiple primes.",
author = "Hanson, {Brandon William} and Vaughan, {Robert Charles} and Ruixiang Zhang",
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