Hecke's theory and the Selberg class

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

Type: Article

Publication Date: 2006-01-01

Citations: 11

DOI: https://doi.org/10.7169/facm/1229442622

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.

Locations

Functiones et Approximatio Commentarii Mathematici - View - PDF

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+	(Almost) primitivity of Hecke L-functions	2007	Giuseppe Molteni Jörn Steuding
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+	The Julia Line of a Riemann-Type Functional Equation {\footnotesize -- Counting Formulae, Dirichlet Polynomial Approximations, and a Weak Gram Law --}	2020	Athanasios Sourmelidis Jörn Steuding Ade Irma Suriajaya
+	Riemann-Type Functional Equations -- Julia Line and Counting Formulae --.	2021	Athanasios Sourmelidis Jörn Steuding Ade Irma Suriajaya
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+	The finiteness of derivation-invariant prime ideals and the algebraic independence of the Eisenstein series	2021	Bo‐Hae Im Wonwoong Lee
+ PDF Chat	A note on Hecke's functional equation and the Selberg class	2009	G. Monti Bragadin Ettore Carletti Alberto Perelli
+	Generalized Atkin Polynomials and Non-Ordinary Hyperelliptic Curves	2012	Matthew Ernest Lane

Works Cited by This (11)

Action	Title	Year	Authors
+	Topics in Classical Automorphic Forms	1997	Henryk Iwaniec
+	�ber die Heckeschen GruppenG(?)II	1974	Armin Leutbecher
+	On the structure of the Selberg class, V: 1 < d < 5/3	2002	Jerzy Kaczorowski Alberto Perelli
+	Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung	1936	E. Hecke
+	Hecke operators on ?0(m)	1970	A. O. L. Atkin Joseph Lehner
+	Introduction to p-adic Numbers and Valuation Theory.	1966	William W. Adams George Bachman
+ PDF Chat	On the Selberg class of Dirichlet series: small degrees	1993	J. Brian Conrey Amit Ghosh
+ PDF Chat	On the structure of the Selberg class, I: 0≤d≤1	1999	Jerzy Kaczorowski Alberto Perelli
+	On Modular Forms With Associated Dirichlet Series	1969	A. P. Ogg
+	Factorization in the extended Selberg class	2003	Jerzy Kaczorowski Alberto Perelli