Classification of L-functions of degree 2 and conductor 1 [article]

J. Kaczorowski, A. Perelli
2022 arXiv   pre-print
We give a full description of the functions F of degree 2 and conductor 1 in the general framework of the extended Selberg class. This is performed by means of a new numerical invariant χ_F, which is easily computed from the data of the functional equation. We show that the value of χ_F gives a precise description of the nature of F, thus providing a sharp form of the classical converse theorems of Hecke and Maass. In particular, our result confirms, in the special case under consideration, the
more » ... conjecture that the functions in the Selberg class are automorphic L-functions.
arXiv:2009.12329v2 fatcat:fno7wngqbvdsvj2a7qejmr2ge4