Equidistribution and independence of Gauss sums
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916242177130496 |
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| author | Rojas-León, Antonio |
| author_facet | Rojas-León, Antonio |
| contents | We prove a general independent equidistribution result for Gauss sums associated to $n$ monomials in $r$ variable multiplicative characters over a finite field, which generalizes several previous equidistribution results for Gauss and Jacobi sums. As an application, we show that any relation satisfied by these Gauss sums must be a combination of the conjugation relation $G(χ)G(\overlineχ)=\pm q$, Galois conjugation invariance and the Hasse-Davenport product formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_12439 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Equidistribution and independence of Gauss sums Rojas-León, Antonio Number Theory Algebraic Geometry 11L05, 11L07, 11T24 We prove a general independent equidistribution result for Gauss sums associated to $n$ monomials in $r$ variable multiplicative characters over a finite field, which generalizes several previous equidistribution results for Gauss and Jacobi sums. As an application, we show that any relation satisfied by these Gauss sums must be a combination of the conjugation relation $G(χ)G(\overlineχ)=\pm q$, Galois conjugation invariance and the Hasse-Davenport product formula. |
| title | Equidistribution and independence of Gauss sums |
| topic | Number Theory Algebraic Geometry 11L05, 11L07, 11T24 |
| url | https://arxiv.org/abs/2207.12439 |