Transcendental numbers and special values of
                    Dirichlet series

Murty, M. Ram

doi:10.1090/conm/701/14148

Cited by 4 publications

(1 citation statement)

References 18 publications

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“…Further, all algebraic relations among these values were determined by Jing Yu [56] and by Chieh-Yu Chang and Jing Yu [23]. These results are very surprising when compared to the extremely limited knowledge we have about the transcendence of values of Riemann’s zeta function at odd positive integers greater than 3 (see section 3 of [44] for a description of known classical results). Goss raised the problem of extending the work of Chang and Yu to a more general setting.…”

Section: Introductionmentioning

confidence: 99%

Algebraic relations among Goss’s zeta values on elliptic curves

Green,

Ngo Dac

2023

Forum of Mathematics, Sigma

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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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Section: Introductionmentioning

confidence: 99%