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Hecke operators in half-integral weight
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Purkait, Soma (2014) Hecke operators in half-integral weight. Journal de Theorie des Nombres de Bordeaux, Volume 26 (Number 1). pp. 233-251. doi:10.5802/jtnb.865 ISSN 1246-7405.
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Official URL: http://dx.doi.org/10.5802/jtnb.865
Abstract
In [6], Shimura introduced modular forms of half-integral weight, their Hecke algebras and their relation to integral weight modular forms via the Shimura correspondence. For modular forms of integral weight, Sturm’s bounds give generators of the Hecke algebra as a module. We also have well-known recursion formulae for the operators $T_{p^\ell }$ with $p$ prime. It is the purpose of this paper to prove analogous results in the half-integral weight setting. We also give an explicit formula for how operators $T_{p^{\ell }}$ commute with the Shimura correspondence.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal de Theorie des Nombres de Bordeaux | ||||
Publisher: | Universite de Bordeaux I, Centre de Recherces en Mathematiques | ||||
ISSN: | 1246-7405 | ||||
Official Date: | 2014 | ||||
Dates: |
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Volume: | Volume 26 | ||||
Number: | Number 1 | ||||
Page Range: | pp. 233-251 | ||||
DOI: | 10.5802/jtnb.865 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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