On the Kohnen-Zagier formula in the case of level \(4p^m\)
type: Item
instance of: scholarly article
title: On the Kohnen-Zagier formula in the case of level \(4p^m\)
zbMATH Open document ID: 1068.11027
author: Hiroshi Sakata
published in: Mathematische Zeitschrift
publication date: 2005-06-02T00:00:00Z
review text: Let \(g\) be a Hecke eigen newform in Kohnen's space of cusp forms of weight \(k + 1/2\) and level \(4N\), \(N\) squarefree. Let \(f\) be the primitive form of weight \(2k\) associated to \(g\) by the Shimura correspondence. The Kohnen-Zagier formula expresses the Fourier-coefficient \(c_g(|D|)\), \((-1)^kD> 0\), as the product of \(L(f,D,k)\) of the \(L\)-function of \(f\) twisted with \(({D\over.})\) with some elementary factors. In the paper under review the author derives an analogous result for \(N= p^m\), \(p\) odd prime. The main difficulty arises from the fact that Kohnen's space does not necessarily have multiplicity one.
Mathematics Subject Classification ID: 11F37
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 11F32
Mathematics Subject Classification ID: 11F67
zbMATH DE Number: 2173661
zbMATH Keywords: Kohnen's space
zbMATH Keywords: Shimura correspondence
zbMATH Keywords: Kohnen-Zagier formula
zbMATH Keywords: newform
zbMATH Keywords: \(L\)-function
reviewed by: Aloys Krieg
MaRDI profile type: Publication
full work available at URL: s00209-004-0740-2
OpenAlex ID: W1974577013
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DOI: 10.1007/S00209-004-0740-2
description: scientific article; zbMATH DE number 2173661