On the trace formula of the Hecke operators and the special values of the second L-functions attached to the Hilbert modular forms
type: Item
instance of: scholarly article
title: On the trace formula of the Hecke operators and the special values of the second L-functions attached to the Hilbert modular forms
zbMATH Open document ID: 0602.10019
DOI: 10.1007/BF01168682
author: Koichi Takase
published in: Manuscripta Mathematica
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155133
review text: In [Modular Funct. of one Var. VI, Lect. Notes Math. 627, 105-169 (1977; Zbl 0372.10017)] \textit{D. Zagier} constructed modular forms for Sl(2, \({\mathbb{Z}})\) with the remarkable property that the Petersson scalar product of these forms with any eigenform f of the Hecke algebra is essentially given by a value of the ''second L-function'' attached to f. Among other things one can get from this construction the Eichler-Selberg trace formula for the action of Hecke operators on the space of cusp forms. In the paper under review the author shows that Zagier's method also works for Hilbert modular forms for totally real number fields with narrow class number one.
Mathematics Subject Classification ID: 11F41
Mathematics Subject Classification ID: 11F67
Mathematics Subject Classification ID: 11F70
zbMATH DE Number: 3970838
zbMATH Keywords: L-function
zbMATH Keywords: trace formula
zbMATH Keywords: Hilbert modular forms
zbMATH Keywords: totally real number fields
zbMATH Keywords: narrow class number one
MaRDI profile type: Publication
cites work: Explicit formula of the traces of Hecke operators for \(\Gamma_0(N)\)
cites work: Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus
cites work: Über Den Bizyklischen Biquadratischen Zahlkörper
cites work: On automorphic forms on \(mathrm{GL}_2\) and Hecke operators
cites work: Automorphic forms and algebraic extensions of number fields
cites work: On discontinuous groups operating on the product of the upper half planes
cites work: Q5517006
cites work: Q4119293
cites work: Q5181775
cites work: Q5579662
cites work: Special Values of Zeta Functions, and Eisenstein Series of Half Integral Weight
description: scientific article; zbMATH DE number 3970838