NDLI: Fundamentals of p-adic multiple L-functions and evaluation of their special values

Content Provider	Springer Nature Link
Author	Komori, Yasushi Furusho, Hidekazu Matsumoto, Kohji Tsumura, Hirofumi
Copyright Year	2016
Abstract	We construct p-adic multiple L-functions in several variables, which are generalizations of the classical Kubota–Leopoldt p-adic L-functions, by using a specific p-adic measure. Our construction is from the p-adic analytic side of view, and we establish various fundamental properties of these functions. (a) Evaluation at non-positive integers: We establish their intimate connection with the complex multiple zeta-functions by showing that the special values of the p-adic multiple L-functions at non-positive integers are expressed by the twisted multiple Bernoulli numbers, which are the special values of the complex multiple zeta-functions at non-positive integers. (b) Multiple Kummer congruences: We extend Kummer congruences for Bernoulli numbers to congruences for the twisted multiple Bernoulli numbers. (c) Functional relations with a parity condition: We extend the vanishing property of the Kubota–Leopoldt p-adic L-functions with odd characters to our p-adic multiple L-functions. (d) Evaluation at positive integers: We establish their close relationship with the p-adic twisted multiple star polylogarithms by showing that the special values of the p-adic multiple L-functions at positive integers are described by those of the p-adic twisted multiple star polylogarithms at roots of unity, which generalizes the result of Coleman in the single variable case.
Ending Page	100
Page Count	62
Starting Page	39
File Format	PDF
ISSN	10221824
e-ISSN	14209020
Journal	Selecta Mathematica
Issue Number	1
Volume Number	23
Language	English
Publisher	Springer International Publishing
Publisher Date	2016-03-26
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Coleman’s p-adic integration theory Zeta functions and $L$ -functions Multiple Dirichlet series and zeta functions and multizeta values Multiple Kummer congruence Other analytic theory (analogues of beta and gamma functions, $p$ -adic integration, etc.) Polylogarithms and relations with $K$ -theory p-adic multiple polylogarithm Mathematics p-adic multiple L-function
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mathematics

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