Functiones et Approximatio Commentarii Mathematici

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

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

https://projecteuclid.org/euclid.facm/1229619652

Digital Object Identifier
doi:10.7169/facm/1229619652

Mathematical Reviews number (MathSciNet)
MR2363825

Zentralblatt MATH identifier
1223.11105

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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