$p$-adic hyperbolic planes and 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 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 کاملp-adic Modular Forms: An Introduction
Serre in the 1970s was the first to formalize such a question on the way to constructing p-adic L-functions, by way of developing the notion of a p-adic modular form to be the p-adic limit of some compatible family of q-expansions of classical modular forms. Katz came along fairly soon afterwards and generalized the theory to a much more geometric context, and showed that Serre’s p-adic forms e...
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...
متن کاملHILBERT MODULAR FORMS AND p-ADIC HODGE THEORY
We consider the p-adic Galois representation associated to a Hilbert modular form. Carayol has shown that, under a certain assumption, its restriction to the local Galois group at a place not dividing p is compatible with the local Langlands correspondence [C2]. In this paper, we show that the same is true for the places dividing p, in the sense of p-adic Hodge theory [Fo], as is shown for an e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1994
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1994-1159195-9