It is well known that Hamburger's converse theorem for the Riemann zeta function does not extend to Dirichlet L-functions, since in this case the functional equations have (in general) many linear independent solutions. Here we characterize the conductors q for which every Dirichlet L-function associated with a primitive character (mod q) is determined, in a general class of Euler products, by its functional equation. Thus, for such conductors we obtain an extension of Hamburger's theorem.
A converse theorem for Dirichlet L-functions
PERELLI, ALBERTO
2010-01-01
Abstract
It is well known that Hamburger's converse theorem for the Riemann zeta function does not extend to Dirichlet L-functions, since in this case the functional equations have (in general) many linear independent solutions. Here we characterize the conductors q for which every Dirichlet L-function associated with a primitive character (mod q) is determined, in a general class of Euler products, by its functional equation. Thus, for such conductors we obtain an extension of Hamburger's theorem.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
