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

Brandon Hanson; Robert C. Vaughan; Ruixiang Zhang

doi:10.1016/j.jnt.2017.03.004

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

Brandon Hanson
, Robert C. Vaughan
, Ruixiang Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	3-16
Number of pages	14
Journal	Journal of Number Theory
Volume	179
DOIs	https://doi.org/10.1016/j.jnt.2017.03.004
State	Published - Oct 2017

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2017.03.004

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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 = "Brandon Hanson and Vaughan, \{Robert C.\} and Ruixiang Zhang",

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doi = "10.1016/j.jnt.2017.03.004",

language = "English (US)",

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AU - Vaughan, Robert C.

AU - Zhang, Ruixiang

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AB - 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.

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UR - https://www.scopus.com/pages/publications/85019577773#tab=citedBy

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M3 - Article

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SP - 3

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JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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