Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 171 (2003), 1-50.
Dirichlet series and automorphic functions associated to a quadratic form
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.
Nagoya Math. J., Volume 171 (2003), 1-50.
First available in Project Euclid: 27 April 2005
Permanent link to this document
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. https://projecteuclid.org/euclid.nmj/1114631909