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