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Explicit application of Waldspurger’s theorem
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Purkait, Soma (2013) Explicit application of Waldspurger’s theorem. LMS Journal of Computation and Mathematics, Volume 16 . pp. 216-245. doi:10.1112/S1461157013000144 ISSN 1461-1570.
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Official URL: http://dx.doi.org/10.1112/S1461157013000144
Abstract
For a given cusp form ϕ of even integral weight satisfying certain hypotheses, Waldspurger’s theorem relates the critical value of the L-function of the nth quadratic twist of ϕ to the nth coefficient of a certain modular form of half-integral weight. Waldspurger’s recipes for these modular forms of half-integral weight are far from being explicit. In particular, they are expressed in the language of automorphic representations and Hecke characters. We translate these recipes into congruence conditions involving easily computable values of Dirichlet characters. We illustrate the practicality of our ‘simplified Waldspurger’ by giving several examples.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | LMS Journal of Computation and Mathematics | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 1461-1570 | ||||
Official Date: | September 2013 | ||||
Dates: |
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Volume: | Volume 16 | ||||
Page Range: | pp. 216-245 | ||||
DOI: | 10.1112/S1461157013000144 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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