Certain values of Hecke \(L\)-functions and generalized hypergeometric functions
type: Item
instance of: scholarly article
title: Certain values of Hecke \(L\)-functions and generalized hypergeometric functions
zbMATH Open document ID: 1261.19004
author: Noriyuki Otsubo
published in: Journal of Number Theory
publication date: 2011-03-03T00:00:00Z
review text: For a smooth projective curve \(X\), one has the regular map from the motivic cohomology group of \(X\), which is given by Milnor \(K\)-groups, to the real Deligne cohomology group. The regular map is closely related to the Beilinson's conjecture on special values of \(L\)-functions of motives. Now let \(X\) be a Fermat curve of degree \(N\). For the cases \(N=3,4\), in this paper the author reformulates the regular maps (after Bloch) and then obtains the special values of \(L\)-functions at \(s=0\) for the Jacobi-sum Hecke characters of the \(N\)th cyclotomic fields over \(\mathbb Q\) by means of generalized hypergeometric functions, respectively.
reviewed by: Feng-Wen An
Mathematics Subject Classification ID: 19F27
Mathematics Subject Classification ID: 33C20
Mathematics Subject Classification ID: 33C65
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11G40
zbMATH DE Number: 5859971
zbMATH Keywords: Fermat curve
zbMATH Keywords: \(L\)-function
zbMATH Keywords: Milnor \(K\)-group
zbMATH Keywords: real Deligne cohomology
zbMATH Keywords: regulator map
zbMATH Keywords: generalized hypergeometric function
zbMATH Keywords: Beilinson conjecture
MaRDI profile type: Publication
full work available at URL: j.jnt.2010.10.002
OpenAlex ID: W2049794548
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DOI: 10.1016/J.JNT.2010.10.002
description: scientific article; zbMATH DE number 5859971