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.
Artin L-functions; automorphic L-functions; Dedekind conjecture; Hecke L-functions; Selberg class; Unique factorization of L-functions;
Settore MAT/05 - Analisi Matematica
2007
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/27883
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