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 flnite 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.
Some remarks on the unique factorization in certain semigroups of classical L-functions / J. Kaczorowski, G. Molteni, A. Perelli. - In: FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI. - ISSN 0208-6573. - 37:2(2007), pp. 263-275. [10.7169/facm/1229619652]
Some remarks on the unique factorization in certain semigroups of classical L-functions
G. Molteni;
2007
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 flnite 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.File | Dimensione | Formato | |
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