Algebraic relations among Goss’s zeta values on elliptic curves

IF 1.2 2区数学 Q1 MATHEMATICS

Forum of Mathematics Sigma Pub Date : 2023-10-05 DOI:10.1017/fms.2023.94

Nathan Green, Tuan Ngo Dac

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引用次数: 3

Abstract

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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椭圆曲线上高斯zeta值的代数关系

2007年Chang和Yu确定了$A=\mathbb F_q[\theta]$的Goss zeta值之间的所有代数关系，也称为Carlitz zeta值。对于一般基环a, Goss提出了确定正整数处的Goss ζ值之间的所有代数关系的问题，但所知甚少。本文发展了一种一般方法，并确定了基环a(定义在$\mathbb F_q$上的椭圆曲线的坐标环)的高斯ζ值之间的所有代数关系。据我们所知，这是第一个解决高斯问题的工作，当基环的类数严格大于1时。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Forum of Mathematics Sigma Mathematics-Statistics and Probability

CiteScore

1.90

自引率

5.90%

发文量

审稿时长

40 weeks

期刊介绍： Forum of Mathematics, Sigma is the open access alternative to the leading specialist mathematics journals. Editorial decisions are made by dedicated clusters of editors concentrated in the following areas: foundations of mathematics, discrete mathematics, algebra, number theory, algebraic and complex geometry, differential geometry and geometric analysis, topology, analysis, probability, differential equations, computational mathematics, applied analysis, mathematical physics, and theoretical computer science. This classification exists to aid the peer review process. Contributions which do not neatly fit within these categories are still welcome. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas will be welcomed. All published papers will be free online to readers in perpetuity.