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On separation of quadratic forms on the imaginary quadratic field in its Hilbert class field

Author: Li-Chien Shen
Journal: Proc. Amer. Math. Soc. 136 (2008), 3061-3067
MSC (2000): Primary 11E25
Published electronically: April 29, 2008
MathSciNet review: 2407068
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Abstract: Let $ K^{(1)}$ be the Hilbert class field of the imaginary quadratic field $ K=Q(\sqrt {d}),d<0.$ We derive the product representations of a class of Dirichlet L-series associated with the character group constructed from the Artin map between the ideal class group of $ K$ and the Galois group $ Gal(K^{(1)}/K)$. The application of the Mellin transform to the product representations of these Dirichlet series yields a family of generating functions for representations of positive integers by the subgroups of the quadratic forms.

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Additional Information

Li-Chien Shen
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611-2082

Keywords: Artin map, Galois group, Hilbert class field, quadratic form
Received by editor(s): March 29, 2007
Received by editor(s) in revised form: July 18, 2007
Published electronically: April 29, 2008
Communicated by: Ken Ono
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.