Mock modular period functions and 𝐿-functions of cusp forms in higher level cases

Choi, SoYoung; Kim, Chang Heon

doi:10.1090/S0002-9939-2014-12073-9

Mock modular period functions and $L$-functions of cusp forms in higher level cases
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Proc. Amer. Math. Soc. 142 (2014), 3369-3386 Request permission

Abstract:

Generalizing the results of Bringmann, Guerzhoy, Kent and Ono, we investigate mock modular period polynomials associated to harmonic Maass forms for $\Gamma _0^+(p)$. In particular, using period relations generated from the period polynomials, we derive congruence relations involving the critical values of modular $L$-functions and show that these congruence relations are indeed equalities by using integral representations of nonholomorphic parts of harmonic Maass forms.

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