منابع مشابه
Modular Forms and - adic Representations ∗
the circumstance that L-functions can be introduced not only in the context of automorphic forms, with which he has had some experience, but also in the context of diophantine geometry. That this circumstance can be the source of deep problems was, I believe, first perceived by E. Artin. He was, to be sure, concerned with forms on GL(1) and with varieties of dimension 0. This remains the only c...
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 کاملSlopes of overconvergent 2-adic modular forms
We explicitly compute all the slopes of the Hecke operator U2 acting on overconvergent 2-adic level 1 cusp forms of weight 0: the nth slope is 1 + 2v((3n)!/n!), where v denotes the 2-adic valuation. We formulate an explicit conjecture about what these slopes should be for weight k forms.
متن کاملSlopes of 3-adic overconvergent modular forms
If r = 12 and (uij) is the matrix of the U operator in the above basis, then the numbers uij satisfy a recurrence formula: there is a p × p matrix M such that uij = ∑p r,s=1Mrsui−r,j−s. Furthermore, M is skew-upper-triangular and constant on off diagonals; and the coefficients uij satisfy uij = jiuji. The case p = 2 is extensively studied in [BC05]. Here the recurrence relation is simple enough...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2014
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2013.10.010