Hypergeometric Properties of Genus 3 Generalized Legendre Curves
Number Theory
2017-05-09 v1
Abstract
Inspired by a result of Manin, we study the relationship between certain period integrals and the trace of Frobenius of genus 3 generalized Legendre curves. We show that both of these properties can be computed in terms of "matching" classical and finite field hypergeometric functions, a phenomenon that has also been observed in elliptic curves and many higher dimensional varieties.
Cite
@article{arxiv.1705.02404,
title = {Hypergeometric Properties of Genus 3 Generalized Legendre Curves},
author = {Heidi Goodson},
journal= {arXiv preprint arXiv:1705.02404},
year = {2017}
}
Comments
13 pages