منابع مشابه
Algebraicity of Singular Values and Arithmetic of Principal Modular Forms
In this thesis, we prove several results on the algebraicity of values of certain modular functions. More precisely, let f(z) be a modular form for the congruence group Γ0(N). We show that f(τ) is an element in the ring class field for the order Oτ corresponding to τ whenever τ is the fixed point of a specific class of matrices in the normalizer of Γ0(N), and provide the explicit Galois action ...
متن کاملDetermination of Modular Forms by Twists of Critical L-values
Contents 0 Introduction 1 1 Preliminaries 4 2 p-power twists 7 3 Quadratic twists 13 4 Generation of coeecient elds by ratios of L-values 20 5 p-adic L-functions 22 6 Forms of half integral weight 25 Bibliography 28 0 Introduction Let f be a normalized holomorphic newform (deened on the upper half plane H) of level N, weight 2k and trivial character. It is given by a Fourier expansion f(z) = P ...
متن کاملProbabilities as Values of Modular Forms and Continued Fractions
Abstract. We consider certain probability problems which are naturally related to integer partitions. We show that the corresponding probabilities are values of classical modular forms. Thanks to this connection, we then show that certain ratios of probabilities are specializations of the Rogers-Ramanujan, and RamanujanSelbergGordon-Göllnitz continued fractions. One particular evaluation depend...
متن کاملExplicit large image theorems for modular forms
Let f be a (cuspidal) newform of weight k 2 and level Γ0(N) with N 1. Ribet proved that, under the assumption that f is non-CM, the residual representations ρ̄f,λ attached to f by Deligne have a large image, in a precise sense, for all but finitely many prime ideals λ. In this paper, we make Ribet’s theorem explicit by proving that the residue characteristics of these finitely many prime ideals ...
متن کاملA Modular Symbol with Values in Cusp Forms
In [B-G1] and [B-G2], Borisov and Gunnells constructed for each level (N > 1) and for each weight (k ≥ 2) a modular symbol with values in Sk(Γ1(N)) using products of Eisenstein series. In this paper we generalize this result by producing a modular symbol (for GL2(Q)!!!) with values in locally constant distributions on M2(Q) taking values in the space of cuspidal power series in two variables (s...
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ژورنال
عنوان ژورنال: Cambridge Journal of Mathematics
سال: 2014
ISSN: 2168-0930,2168-0949
DOI: 10.4310/cjm.2014.v2.n1.a3