Converse theorems for automorphic distributions and Maass forms of level N

  • Tadashi Miyazaki
  • Fumihiro Sato
  • Kazunari SugiyamaEmail author
  • Takahiko Ueno


We investigate the relationship between L-functions satisfying certain functional equations, summation formulas of Ferrar–Suzuki type and Maass forms of integral and half-integral weight. Summation formulas of Ferrar–Suzuki type can be viewed as an automorphic property of distribution vectors of non-unitary principal series representations of the double covering group of SL(2). Our goal is converse theorems for automorphic distributions and Maass forms of level N characterizing them by analytic properties of the associated L-functions. As an application of our converse theorems, we construct Maass forms from the two-variable zeta functions related to quadratic forms studied by Peter and the fourth author.


Maass forms Automorphic distributions Converse theorem Summation formula Prehomogeneous zeta functions 



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Authors and Affiliations

  1. 1.Department of Mathematics, College of Liberal Arts and SciencesKitasato UniversitySagamiharaJapan
  2. 2.Institute for Mathematics and Computer ScienceTsuda CollegeKodaira-shiJapan
  3. 3.Department of MathematicsChiba Institute of TechnologyNarashinoJapan
  4. 4.Medical InformaticsSt. Marianna University School of MedicineKawasakiJapan

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