### 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) |
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Pages (from-to) | 3-16 |

Number of pages | 14 |

Journal | Journal of Number Theory |

Volume | 179 |

DOIs | |

State | Published - Oct 1 2017 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

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**The least number with prescribed Legendre symbols and representation by binary quadratic forms of small discriminant.** / Hanson, Brandon William; Vaughan, Robert Charles; Zhang, Ruixiang.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The least number with prescribed Legendre symbols and representation by binary quadratic forms of small discriminant

AU - Hanson, Brandon William

AU - Vaughan, Robert Charles

AU - Zhang, Ruixiang

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85019577773&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019577773&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2017.03.004

DO - 10.1016/j.jnt.2017.03.004

M3 - Article

VL - 179

SP - 3

EP - 16

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -