Algebraic Relations among Goss's Zeta Values on Elliptic Curves

2020/04/17 by Green, Nathan, Dac, Tuan Ngo
#11G09 #11J93 #11M38 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2004.08461

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.

Related

• Zeros of the Goss zeta function
• Special zeta values using tensor powers of Drinfeld modules
• Zeta-functions of Curves over Finite Fields
• Arithmetic equivalence for function fields, the Goss zeta function and a generalization
• The Riemann Hypothesis for the Goss zeta function for F_q[T]