Values of \(p\)-adic \(L\)-functions at positive integers and \(p\)-adic log multiple gamma functions
type: Item
instance of: scholarly article
title: Values of \(p\)-adic \(L\)-functions at positive integers and \(p\)-adic log multiple gamma functions
zbMATH Open document ID: 0809.11067
author: Hideo Imai
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1994-04-12T00:00:00Z
review text: In the late 1970s, Diamond expressed special values of \(p\)-adic \(L\)- functions at positive integers in terms of the \(p\)-adic log gamma function. In this paper, the author extends the work of Diamond to a class of \(p\)-adic \(L\)-functions in several variables (previously defined by the author). He expresses special values of these \(L\)-functions at positive integers in terms of \(p\)-adic log multiple gamma functions. Since the \(p\)-adic \(L\)-function of a totally real number field can be expressed in terms of these multivariable \(p\)-adic \(L\)-functions, their special values at positive integers can also be expressed in this manner.
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R42
Mathematics Subject Classification ID: 11S80
zbMATH DE Number: 549622
zbMATH Keywords: special values of \(p\)-adic \(L\)-functions at positive integers
zbMATH Keywords: \(p\)-adic \(L\)-functions in several variables
zbMATH Keywords: \(p\)-adic log multiple gamma functions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225845
OpenAlex ID: W2045501726
cites work: Values at negative integers of zeta functions and \(p\)-adic zeta functions
cites work: Q3859899
cites work: Residue at \(s=1\) of \(p\)-adic zeta functions
cites work: The p-Adic Log Gamma Function and p-Adic Euler Constants
cites work: On the values of p-adic L-functions at positive integers
cites work: On the behavior of \(p\)-adic \(L\)-functions at \(s=0\)
cites work: On the values at rational integers of the p-adic Dirichlet L functions
cites work: On the construction of p-adic L-functions
cites work: Lectures on P-Adic L-Functions. (AM-74)
cites work: A new proof of certain formulas for p-adic L-functions
cites work: Q3995821
cites work: Q4065637
cites work: Q4156858
cites work: Q4138810
DOI: 10.2748/TMJ/1178225845
description: scientific article; zbMATH DE number 549622