It is conjectured that the Selberg class of L-functions is a unique factorization semigroup. It is not clear if such a property should hold for the extended Selberg class as well. Here we prove the unique factorization of certain subsemigroups of the extended Selberg class. These semigroups are generated by the functions of degree 0 and 1. We also consider extensions of such results and applications to classical L-functions.
Unique factorization results for semigroups of L-functions
PERELLI, ALBERTO
2008-01-01
Abstract
It is conjectured that the Selberg class of L-functions is a unique factorization semigroup. It is not clear if such a property should hold for the extended Selberg class as well. Here we prove the unique factorization of certain subsemigroups of the extended Selberg class. These semigroups are generated by the functions of degree 0 and 1. We also consider extensions of such results and applications to classical L-functions.
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