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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Algebraic independence of the Carlitz period and the positive characteristic multizeta values at $n$ and $(n,n)$
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by Yoshinori Mishiba PDF
Proc. Amer. Math. Soc. 143 (2015), 3753-3763 Request permission

Abstract:

Let $k$ be the rational function field over the finite field of $q$ elements and $\overline {k}$ its fixed algebraic closure. In this paper, we study algebraic relations over $\overline {k}$ among the fundamental period $\widetilde {\pi }$ of the Carlitz module and the positive characteristic multizeta values $\zeta (n)$ and $\zeta (n,n)$ for an β€œodd” integer $n$, where we say that $n$ is β€œodd” if $q-1$ does not divide $n$. We prove that these three elements are either algebraically independent over $\overline {k}$ or satisfy some simple relation over $k$. We also prove that if $2n$ is β€œodd”, then these three elements are algebraically independent over $\overline {k}$.
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Additional Information
  • Yoshinori Mishiba
  • Affiliation: Department of General Education, Oyama National College of Technology, 771 Nakakuki, Oyama, Tochigi, 323-0806, Japan
  • Email: mishiba@oyama-ct.ac.jp
  • Received by editor(s): August 21, 2013
  • Received by editor(s) in revised form: April 24, 2014
  • Published electronically: February 25, 2015
  • Additional Notes: The author was partially supported by the JSPS Research Fellowships for Young Scientists
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 3753-3763
  • MSC (2010): Primary 11J93; Secondary 11G09, 11M38
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12532-4
  • MathSciNet review: 3359567