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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
Extract
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].
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1989
Footnotes
The work on this paper was partially supported by NSF Grant DMS 8601130.
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