Abstract
In this paper, we consider p-adic limits of β −n g|U n2 for half-integral weight weakly holomorphic Hecke eigenforms g with eigenvalue λp = β + β � under T p2 and prove that these equal classical Hecke eigenforms of the same weight. This result parallels the integral weight case, but requires a much more careful investigation due to a more complicated structure of half-integral weight weakly holomorphic Hecke eigenforms.
Highlights
Introduction and statement of the resultsIn this paper, we establish a p-adic relation between half-integral weight weakly holomorphic modular forms and classical half-integral weight holomorphic modular forms
In this paper, we consider p-adic limits of β−ng|Upn2 for half-integral weight weakly holomorphic Hecke eigenforms g with eigenvalue λp = β + β under Tp2 and prove that these equal classical Hecke eigenforms of the same weight
1 Introduction and statement of the results In this paper, we establish a p-adic relation between half-integral weight weakly holomorphic modular forms and classical half-integral weight holomorphic modular forms
Summary
Introduction and statement of the resultsIn this paper, we establish a p-adic relation between half-integral weight weakly holomorphic modular forms and classical half-integral weight holomorphic modular forms. The construction of half-integral weight weakly holomorphic Hecke eigenforms is much more delicate. The fact that the resulting p-adic relations parallel those in the integral weight case strongly supports the definition of half-integral weight weakly holomorphic Hecke eigenforms found in [4].
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