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Shimura correspondence for level and the central values of L-series

✍ Scribed by Ariel Pacetti; Gonzalo Tornaría

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
216 KB
Volume
124
Category
Article
ISSN
0022-314X

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✦ Synopsis

Given a weight 2 and level p 2 modular form f , we construct two weight 3/2 modular forms (possibly zero) of level 4p 2 and non-trivial character mapping to f via the Shimura correspondence. Then we relate the coefficients of the constructed forms to the central value of the L-series of certain imaginary quadratic twists of f . Furthermore, we give a general framework for our construction that applies to any order in definite quaternion algebras, with which one can, in principle, construct weight 3/2 modular forms of any level, provided one knows how to compute ideal classes representatives.

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