On \(p\)-adic \(q\)-\(L\)-functions and sums of powers
type: Item
instance of: scholarly article
title: On \(p\)-adic \(q\)-\(L\)-functions and sums of powers
zbMATH Open document ID: 1007.11073
DOI: 10.1016/S0012-365X(01)00293-X
author: Taekyun Kim
published in: Discrete Mathematics
publication date: 2002-08-29T00:00:00Z
review text: Let \(q\in \mathbb C_p\), \(|q-1|_p<p^{-1/(p-1)}\). The author finds an explicit expression for the sum of \(\frac{q^j}{[j]^r}\) taken over natural numbers \(j\), such that \(1\leq j\leq np\) and \(j\) is prime to \(p\), via a \(q\)-analog of the \(p\)-adic \(L\)-functions. Here \([j]=\frac{1-q^j}{1-q}\). As special cases and corollaries, this result includes earlier ones by Andrews, Washington, Barsky, and others. A \(q\)-analog, for \(q\in \mathbb C\), \(|q|<1\), is also found for a recurrence for Bernoulli numbers obtained by \textit{E. Y. Deeba} and \textit{D. M. Rodriguez} [Am. Math. Mon. 98, 423-426 (1991; Zbl 0743.11012)].
Mathematics Subject Classification ID: 11S80
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 05A30
zbMATH DE Number: 1792423
zbMATH Keywords: \(p\)-adic \(q\)-\(L\)-function
zbMATH Keywords: \(q\)-Bernoulli numbers
zbMATH Keywords: \(q\)-series
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
full work available at URL: s0012-365x(01)00293-x
OpenAlex ID: W2015741724
description: scientific article; zbMATH DE number 1792423