Functiones et Approximatio Commentarii Mathematici
- Funct. Approx. Comment. Math.
- Volume 37, Number 2 (2007), 263-275.
Some remarks on the unique factorization in certain semigroups of classical $L$-functions
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.
Funct. Approx. Comment. Math., Volume 37, Number 2 (2007), 263-275.
First available in Project Euclid: 18 December 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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