Algebraic relations among Goss's zeta values on elliptic curves

Green, Nathan; Ngo Dac, Tuan

doi:10.1017/fms.2023.94

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Algebraic relations among Goss's zeta values on elliptic curves

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Ngo Dac, Tuan
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.48550/arXiv.2004.08461
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https://doi.org/10.1017/fms.2023.94
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Citation

Green, N., & Ngo Dac, T. (2023). Algebraic relations among Goss's zeta values on elliptic curves. Forum of Mathematics, Sigma, 11: e90. doi:10.1017/fms.2023.94.

Cite as: https://hdl.handle.net/21.11116/0000-000D-C358-4

Abstract

In 2007 Chang and Yu determined all the algebraic relations among Goss’s zeta values for A=Fq[θ], 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 Fq. To our knowledge, this is the first work tackling Goss’s problem when the base ring has class number strictly greater than 1.