Moments of Gaussian Periods and Modified Fermat Curves
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2021
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912236437504000 |
|---|---|
| author | Garcia, Stephan Ramon Lorenz, Brian Todd, George |
| author_facet | Garcia, Stephan Ramon Lorenz, Brian Todd, George |
| contents | We use supercharacter theory to study moments of Gaussian periods. For $p-1=dk$ and fixed $k$, we compute the fourth absolute moments for all but finitely many primes $p$. For $d$ fixed, we relate the fourth absolute moments to the number of rational points on modified Fermat curves. For small $d$, this relation is in terms of a single curve. For larger $d$, we provide both exact formulas using families of modified Fermat curves and bounds via Hasse--Weil. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_13886 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Moments of Gaussian Periods and Modified Fermat Curves Garcia, Stephan Ramon Lorenz, Brian Todd, George Number Theory 11L05, 11L99, 11T22, 11T23, 11T24 We use supercharacter theory to study moments of Gaussian periods. For $p-1=dk$ and fixed $k$, we compute the fourth absolute moments for all but finitely many primes $p$. For $d$ fixed, we relate the fourth absolute moments to the number of rational points on modified Fermat curves. For small $d$, this relation is in terms of a single curve. For larger $d$, we provide both exact formulas using families of modified Fermat curves and bounds via Hasse--Weil. |
| title | Moments of Gaussian Periods and Modified Fermat Curves |
| topic | Number Theory 11L05, 11L99, 11T22, 11T23, 11T24 |
| url | https://arxiv.org/abs/2112.13886 |