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Converse theorem

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In the matheamtical theory of automorphic forms, a converse theorem gives sufficient conditions for a Dirichlet series to come from an automorphic form.

Weil's converse theorem

The first higher dimensional converse theorem was proved by Weil (1967)

References

  • Ogg, Andrew (1969), Modular forms and Dirichlet series, W. A. Benjamin, Inc., New York-Amsterdam, MR0256993
  • Weil, André (1967), "Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen", Mathematische Annalen, 168: 149–156, doi:10.1007/BF01361551, ISSN 0025-5831, MR0207658
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