Geodesic
Algebraic relations among Goss’s zeta values on elliptic curves
Forum of Mathematics, Sigma, Tome 11 (2023)

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In 2007 Chang and Yu determined all the algebraic relations among Goss’s zeta values for $A=\mathbb F_q[\theta ]$, also known as the Carlitz zeta values. Goss raised the problem of determining all algebraic relations among Goss’s zeta values at positive integers for a general base ring A, but very little is known. In this paper, we develop a general method, and we determine all algebraic relations among Goss’s zeta values for the base ring A which is the coordinate ring of an elliptic curve defined over $\mathbb F_q$. To our knowledge, this is the first work tackling Goss’s problem when the base ring has class number strictly greater than 1. 
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     title = {Algebraic relations among {Goss{\textquoteright}s} zeta values on elliptic curves},
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Nathan Green; Tuan Ngo Dac. Algebraic relations among Goss’s zeta values on elliptic curves. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.94

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