Algebraic relations among Goss's zeta values on elliptic curves
Résumé
In 2007 Chang and Yu determined all the algebraic relations among Goss's zeta values for A = F_q[θ] 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 F_q. 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.
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