Algebraic Relations among Goss's Zeta Values on Elliptic Curves
Number Theory
2020-04-21 v1
Abstract
In 2007 Chang and Yu determined all the algebraic relations among Goss's zeta values for the rational function field - these are also known as the Carlitz zeta values. Goss raised the problem about algebraic relations among Goss's zeta values for a general base ring A, but very little is known. In this paper we develop a general method and determine all algebraic relations among Goss's zeta values for the base ring A attached to an elliptic curve over a finite field. To our knowledge, these are the first non-trivial solutions of Goss's problem for a base ring whose class number is strictly greater than 1.
Keywords
Cite
@article{arxiv.2004.08461,
title = {Algebraic Relations among Goss's Zeta Values on Elliptic Curves},
author = {Nathan Green and Tuan Ngo Dac},
journal= {arXiv preprint arXiv:2004.08461},
year = {2020}
}
Comments
41 pages