Some remarks on the unique factorization in certain semigroups of classical $L$-functions
Kaczorowski, Jerzy ; Molteni, Giuseppe ; Perelli, Alberto
Funct. Approx. Comment. Math., Tome 37 (2007) no. 1, p. 263-275 / Harvested from Project Euclid
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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.
Publié le : 2007-09-15
Classification:  unique factorization of $L$-functions,  Artin $L$-functions,  automorphic $L$-functions,  Hecke $L$-functions,  Selberg class,  Dedekind conjecture,  11S40,  11R42,  11M99 
@article{1229619652,
     author = {Kaczorowski, Jerzy and Molteni, Giuseppe and Perelli, Alberto},
     title = {Some remarks on the unique factorization in certain semigroups of classical $L$-functions},
     journal = {Funct. Approx. Comment. Math.},
     volume = {37},
     number = {1},
     year = {2007},
     pages = { 263-275},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1229619652}
}

Kaczorowski, Jerzy; Molteni, Giuseppe; Perelli, Alberto. Some remarks on the unique factorization in certain semigroups of classical $L$-functions. Funct. Approx. Comment. Math., Tome 37 (2007) no. 1, pp.  263-275. http://gdmltest.u-ga.fr/item/1229619652/