Algebraic relations among Goss’s zeta values on elliptic curves

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...

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Veröffentlicht in:Forum of mathematics. Sigma 2023-01, Vol.11, p.1-40, Article e90
Hauptverfasser: Green, Nathan, Ngo Dac, Tuan
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2023.94