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Explicit formulas for local factors in the Euler products for Eisenstein series1)

Published online by Cambridge University Press:  22 January 2016

Paul Feit
Paul Feit*
Affiliation:
Department of Mathematics University of Chicago, Chicago, Illinois60637
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Our objective is to prove that certain Dirichlet series (in our variable q−s), which are defined by infinite sums, can be expressed as a product of an explicit rational function in q−s times an unknown polynomial M in q−s Moreover we show that M(q−s) is 1 if a simple condition is met. The Dirichlet series appear in the Euler products of Fourier coefficients for Eisenstein series. The series discussed below generalize the functions α0(N, q−s) used by Shimura in [12], and the theorem is an extension of Kitaoka’s result [5].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 113 , March 1989 , pp. 37 - 87
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

Footnotes

1)

The work on this paper was partially supported by NSF Grant DMS 8601130.

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