Trace formula and trace identity of twisted Hecke operators on the spaces of cusp forms of weight \(k+1/2\) and level \(32M\)
type: Item
instance of: scholarly article
title: Trace formula and trace identity of twisted Hecke operators on the spaces of cusp forms of weight \(k+1/2\) and level \(32M\)
zbMATH Open document ID: 1238.11054
author: Masaru Ueda
published in: Proceedings of the Japan Academy. Series A
publication date: 2009-04-27T00:00:00Z
review text: In a sequence of papers [J. Math. Kyoto Univ. 28, No. 3, 505--555 (1988; Zbl 0673.10021) and Jap. J. Math., New Ser. 17, No. 1, 83--135 (1991; Zbl 0742.11031)] among others, the author studied trace formulae for Hecke operators on spaces of cusp forms of half-integral weight \(k + \frac12\), level \(N\) and character \(\chi\). In the present note a case is discussed which was not treated before: For level \(N = 32 M\) with \(M\) odd, these spaces are not generally closed under twisted Hecke operators \(R_{\psi} \tilde{T}(n^{2})\). However, they are closed under certain conditions on the conductors of \(\chi\) and \(\psi\), and the author presents explicit trace formulae for these cases. The details and proofs are announced to appear elsewhere.
reviewed by: Günter Köhler
Mathematics Subject Classification ID: 11F37
Mathematics Subject Classification ID: 11F25
zbMATH DE Number: 5547614
zbMATH Keywords: trace formula
zbMATH Keywords: twisting operator
zbMATH Keywords: half-integral weight
zbMATH Keywords: trace identity
zbMATH Keywords: Hecke operator
zbMATH Keywords: cusp form
MaRDI profile type: Publication
full work available at URL: pjaa.85.11
OpenAlex ID: W2012584411
cites work: Q4693061
cites work: On modular forms of half integral weight
cites work: The decomposition of the spaces of cusp forms of half-integral weight and trace formula of Hecke operators
cites work: Q3979925
cites work: Trace formula of twisting operators of half-integral weight in the case of even conductors.
cites work: Trace identities of twisted Hecke operators on the spaces of cusp forms of half-integral weights
cites work: Q4497394
DOI: 10.3792/PJAA.85.11
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description: scientific article; zbMATH DE number 5547614