Functiones et Approximatio Commentarii Mathematici

Hecke's theory and the Selberg class

Jerzy Kaczorowski, Giuseppe Molteni, Alberto Perelli, Jörn Steuding, and Jürgen Wolfart

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Abstract

Roughly speaking, we prove that the Hecke $L$-functions associated with the cusp forms of the Hecke groups $\mathsf{G}(\lambda)$ belong to the extended Selberg class, and for $\lambda \leq 2$ we characterize the Hecke $L$-functions belonging to the Selberg class.

Article information

Source
Funct. Approx. Comment. Math., Volume 35 (2006), 183-193.

Dates
First available in Project Euclid: 16 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229442622

Digital Object Identifier
doi:10.7169/facm/1229442622

Mathematical Reviews number (MathSciNet)
MR2206240

Zentralblatt MATH identifier
1196.11069

Subjects
Primary: 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations
Secondary: 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}

Keywords
Selberg class Hecke theory

Citation

Kaczorowski, Jerzy; Molteni, Giuseppe; Perelli, Alberto; Steuding, Jörn; Wolfart, Jürgen. Hecke's theory and the Selberg class. Funct. Approx. Comment. Math. 35 (2006), 183--193. doi:10.7169/facm/1229442622. https://projecteuclid.org/euclid.facm/1229442622


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