1. On the functional equation of the normalized Shintani L-function of several variables
- Author
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Minoru Hirose and Nobuo Sato
- Subjects
Integral representation ,Mathematics - Number Theory ,Generalization ,Mathematics::Number Theory ,General Mathematics ,Mathematics::Classical Analysis and ODEs ,Special values ,Riemann zeta function ,Algebra ,symbols.namesake ,11M32 (Primary) 11M35 (Secondary) ,Functional equation ,FOS: Mathematics ,symbols ,Number Theory (math.NT) ,L-function ,Mathematics::Representation Theory ,Mathematics - Abstract
In this paper, we introduce the normalized Shintani L-function of several variables by an integral representation and prove its functional equation. The Shintani L-function is a generalization to several variables of the Hurwitz-Lerch zeta function and the functional equation given in this paper is a generalization of the functional equation of Hurwitz-Lerch zeta function. In addition to the functional equation, we give special values of the normalized Shintani L-function at non-positive integers and some positive integers.
- Published
- 2015
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