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Dirichlet series and automorphic functions associated to a quadratic form

Published online by Cambridge University Press:  22 January 2016

Manfred Peter
Manfred Peter*
Affiliation:
Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, D-79104 Freiburg, Germany, manfred.peter@math.uni-freiburg.de
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Abstract

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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.

Keywords

11F3711F6611E45
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 171 , 2003 , pp. 1 - 50
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

References

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