Computations with classical and p-adic modular forms
نویسندگان
چکیده
منابع مشابه
Dimension Variation of Classical and p-adic Modular Forms
A quadratic bound is obtained for a conjecture of Gouv^ ea-Mazur on arithmetic variation of dimensions of classical and p-adic modular forms.
متن کاملCLASSICAL AND p-ADIC MODULAR FORMS ARISING FROM THE BORCHERDS EXPONENTS OF OTHER MODULAR FORMS
Abstract. Let f(z) = q ∏∞ n=1(1−q) be a modular form on SL2(Z). Formal logarithmic differentiation of f yields a q-series g(z) := h −∞n=1 ∑ d|n c(d)dq n whose coefficients are uniquely determined by the exponents of the original form. We provide a formula, due to Bruinier, Kohnen, and Ono for g(z) in terms of the values of the classical j-function at the zeros and poles of f(z). Further, we giv...
متن کاملMOCK 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...
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ژورنال
عنوان ژورنال: LMS Journal of Computation and Mathematics
سال: 2011
ISSN: 1461-1570
DOI: 10.1112/s1461157011000155