Nagoya Mathematical Journal

Dirichlet series and automorphic functions associated to a quadratic form

Manfred Peter

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Starting from the reciprocity law for Gaussian sums attached to an integral quadratic form we prove functional equations for a new kind of Dirichlet series in two variables. For special values of one variable they are of Hecke type with respect to the other variable. With Weil's converse theorem we derive automorphic functions which generalize Siegel's genus invariant and the automorphic functions of Cohen and Zagier.

Article information

Nagoya Math. J., Volume 171 (2003), 1-50.

First available in Project Euclid: 27 April 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F37: Forms of half-integer weight; nonholomorphic modular forms
Secondary: 11E45: Analytic theory (Epstein zeta functions; relations with automorphic 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations


Peter, Manfred. Dirichlet series and automorphic functions associated to a quadratic form. Nagoya Math. J. 171 (2003), 1--50.

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