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Shimura correspondence for level p^2 and the central values of L-series

Ariel Pacetti·Gonzalo Tornaría
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Abstract

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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Ariel Pacetti, Gonzalo Tornaría. 2006-06-23. Shimura correspondence for level p^2 and the central values of L-series. https://doi.org/10.1016/j.jnt.2006.10.011

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