Functiones et Approximatio Commentarii Mathematici

Some remarks on the unique factorization in certain semigroups of classical $L$-functions

Jerzy Kaczorowski, Giuseppe Molteni, and Alberto Perelli

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Abstract

In this note we investigate problems related to the unique factorization of some semigroups of classical $L$-functions. The semigroups of Artin and automorphic $L$-functions as well as the semigroup generated by the Hecke $L$-functions of finite order are studied. The main result of the paper shows that in the latter semigroup the unique factorization into primitive elements does not hold. This closes a possible way of attacking the famous Dedekind conjecture concerning the divisibility of the Dedekind zeta functions.

Article information

Source
Funct. Approx. Comment. Math., Volume 37, Number 2 (2007), 263-275.

Dates
First available in Project Euclid: 18 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229619652

Digital Object Identifier
doi:10.7169/facm/1229619652

Mathematical Reviews number (MathSciNet)
MR2363825

Zentralblatt MATH identifier
1223.11105

Subjects
Primary: 11S40: Zeta functions and $L$-functions [See also 11M41, 19F27]
Secondary: 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27] 11M99: None of the above, but in this section

Keywords
unique factorization of $L$-functions Artin $L$-functions automorphic $L$-functions Hecke $L$-functions Selberg class Dedekind conjecture

Citation

Kaczorowski, Jerzy; Molteni, Giuseppe; Perelli, Alberto. Some remarks on the unique factorization in certain semigroups of classical $L$-functions. Funct. Approx. Comment. Math. 37 (2007), no. 2, 263--275. doi:10.7169/facm/1229619652. https://projecteuclid.org/euclid.facm/1229619652


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