A geometric perspective on p-adic properties of mock modular forms
نویسندگان
چکیده
منابع مشابه
MOCK MODULAR FORMS AS p-ADIC MODULAR FORMS
In this paper, we consider the question of correcting mock modular forms in order to obtain p-adic modular forms. In certain cases we show that a mock modular form M is a p-adic modular form. Furthermore, we prove that otherwise the unique correction of M is intimately related to the shadow of M.
متن کاملp-Adic coupling of mock modular forms and shadows.
A "mock modular form" is the holomorphic part of a harmonic Maass form f. The nonholomorphic part of f is a period integral of its "shadow," a cusp form g. A direct method for relating the coefficients of shadows and mock modular forms is not known. We solve these problems when the shadow is an integer weight newform. Our solution is p-adic, and it relies on our definition of an algebraic "regu...
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We examine the Fourier coefficients of modular forms in a canonical basis for the spaces of weakly holomorphic modular forms of weights 4, 6, 8, 10, and 14, and show that these coefficients are often highly divisible by the primes 2, 3, and 5.
متن کاملBounding slopes of p-adic modular forms
Let p be prime, N be a positive integer prime to p, and k be an integer. Let Pk(t) be the characteristic series for Atkin’s U operator as an endomorphism of p-adic overconvergent modular forms of tame level N and weight k. Motivated by conjectures of Gouvêa and Mazur, we strengthen a congruence in [W] between coefficients of Pk and Pk′ for k ′ p-adically close to k. For p − 1 | 12, N = 1, k = 0...
متن کاملPerspectives on mock modular forms
Article history: Received 30 August 2016 Received in revised form 2 February 2017 Accepted 20 February 2017 Available online 24 February 2017 Communicated by D. Goss
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ژورنال
عنوان ژورنال: Research in the Mathematical Sciences
سال: 2017
ISSN: 2197-9847
DOI: 10.1186/s40687-017-0095-z