Twists, Euler products and a converse theorem for L-functions of degree 2

• Jerzy Kaczorowski ^[1] ; Alberto Perelli ^[2]
  1. [1] Adam Mickiewicz University in Poznań

     Adam Mickiewicz University in Poznań

     Poznań, Polonia

     
  2. [2] Università di Genova, Italia
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 2, 2015, págs. 441-480
• Idioma: inglés
• Enlaces
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• Resumen

  • We prove a general result relating the shape of the Euler product of an L-function to the analytic properties of the linear twists of the L-function itself. Then, by a sharp form of the transformation formula for linear twists, we check the required analytic properties in the case of L-functions of degree 2 and conductor 1 in the Selberg class. Finally we prove a converse theorem, showing that ⇣(s)2 is the only member of the Selberg class with degree 2, conductor 1 and a pole at s = 1.