The least number with prescribed Legendre symbols and representation by binary quadratic forms of small discriminant
| Autor: | Brandon Hanson, Robert C. Vaughan, Ruixiang Zhang |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory 010102 general mathematics Quadratic reciprocity 010103 numerical & computational mathematics Legendre symbol Legendre's equation 01 natural sciences Power residue symbol Combinatorics symbols.namesake Quadratic integer ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION symbols Binary quadratic form Kronecker symbol Quadratic field 0101 mathematics Mathematics |
| Zdroj: | Journal of Number Theory. 179:3-16 |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2017.03.004 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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