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 βoddβ integer $n$, where we say that $n$ is βoddβ 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 βoddβ, then these three elements are algebraically independent over $\overline {k}$.References
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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