\(p\)-adic limits of Shintani generating functions for a real quadratic field
type: Item
instance of: scholarly article
title: \(p\)-adic limits of Shintani generating functions for a real quadratic field
zbMATH Open document ID: 0861.11065
published in: Journal of Number Theory
publication date: 1997-05-12T00:00:00Z
review text: In the paper [\textit{T. Shintani}, J. Fac. Sci. Univ. Tokyo, Sect. I A 23, No. 2, 393-417 (1976; Zbl 0349.12007)], special values were evaluated at non-positive integers of zeta functions for a totally real algebraic number field \(F\) by introducing a kind of generating functions. These evaluations are associated to ``cone decompositions'' in \(F\otimes \mathbb{R}\) which, however, seem rather noncanonical for \(F\neq\mathbb{Q}\). The author of this paper introduces new generating functions by passing to a certain \(p\)-adic limit in the case of a real quadratic field \(F\) with \(h_+ (F) =1\) motivated by Iwasawa Theory and \(p\)-adic \(L\)-functions. In this paper, the author investigates these limiting functions, showing that they possess several interesting properties not shared by those of Shintani.
Mathematics Subject Classification ID: 11R42
Mathematics Subject Classification ID: 11R23
zbMATH DE Number: 913834
zbMATH Keywords: \(p\)-adic limit
zbMATH Keywords: \(p\)-adic \(L\)-functions
zbMATH Keywords: generating functions
zbMATH Keywords: real quadratic field
author: David Solomon
reviewed by: Masakazu Muro
MaRDI profile type: Publication
full work available at URL: jnth.1996.0091
OpenAlex ID: W1968793350
DOI: 10.1006/JNTH.1996.0091
description: scientific article; zbMATH DE number 913834