A converse theorem for Dirichlet -functions

  • Jerzy Kaczorowski

    Adam Mickiewicz University, Poznan, Poland
  • Giuseppe Molteni

    Università di Milano, Italy
  • Alberto Perelli

    Università di Genova, Italy


It is known that the space of solutions (in a suitable class of Dirichlet series with continuation over ) of the functional equation of a Dirichlet -function has dimension as soon as the conductor of is at least 4. Hence the Dirichlet -functions are not characterized by their functional equation for . Here we characterize the conductors q such that for every primitive character , is the only solution with an Euler product in the above space. It turns out that such conductors are of the form with any square-free coprime to 6 and finitely many and .

Cite this article

Jerzy Kaczorowski, Giuseppe Molteni, Alberto Perelli, A converse theorem for Dirichlet -functions. Comment. Math. Helv. 85 (2010), no. 2, pp. 463–483

DOI 10.4171/CMH/202