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

Jerzy Kaczorowski, Giuseppe Molteni, Alberto Perelli
2007 Functiones et Approximatio Commentarii Mathematici  
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.
doi:10.7169/facm/1229619652 fatcat:7dgrzekkgzf47p5upaaaoggv3a