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- Title
On ∞-adic and v-adic multiple zeta functions in positive characteristic.
- Authors
Matsuzuki, Daichi
- Abstract
In this paper, we pursue positive characteristic analogs of the results of Furusho, Komori, Matsumoto, and Tsumura on p -adic multiple L -functions. We consider ∞ -adic and v -adic multiple zeta functions concerned by Anglès, Ngo Dac, and Tavares Ribeiro. Our main results in this paper consist of: (1) integral expressions of special values of ∞ -adic multiple zeta functions, (2) integral expressions of v -adic multiple zeta functions themselves that are similar to those of p -adic multiple L -functions, (3) Kummer-type congruences for the special values of v -adic multiple zeta functions at integers, (4) relationships between special values of ∞ -adic and those of v -adic multiple zeta functions at negative integers, and (5) orthogonal properties of multiple zeta functions and multiple zeta star functions.
- Subjects
ZETA functions; CHARACTERISTIC functions; RIEMANN hypothesis
- Publication
International Journal of Number Theory, 2023, Vol 19, Issue 9, p2263
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042123501117