Parité des valeurs propres des opérateurs de Hecke.
For any non-square 1 < D ≡ 0,1 (mod 4), Zagier defined . Here we use the theory of periods to give identities and congruences which relate various values of .
Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coefficients of a certain mock theta function studied by the first author,...
Our aim in this paper is to prove congruences between on the one hand certain eigenforms of level and weight greater than 2 and on the other hand twists of eigenforms of level and weight 2. One knows a priori that such congruences exist; the novelty here is that we determine the character of the form of weight 2 and the twist in terms of the slope of the higher weight form, i.e., in terms of the valuation of its eigenvalue for . Curiously, we also find a relation between the leading terms of...
Suppose that f is an elliptic modular form with integral coefficients. Sturm obtained bounds for a nonnegative integer n such that every Fourier coefficient of f vanishes modulo a prime p if the first n Fourier coefficients of f are zero modulo p. In the present note, we study analogues of Sturm's bounds for Siegel modular forms of genus 2. As an application, we study congruences involving an analogue of Atkin's U(p)-operator for the Fourier coefficients of Siegel modular forms of genus 2.
On donne une nouvelle condition suffisante pour l’existence des mesures -adiques admissibles obtenues à partir de suites de distributions à valeurs dans les espaces de formes modulaires. On utilise la projection caractéristique sur le sous-espace primaire associé à une valeur propre non nulle de l’opérateur d’Atkin. Notre condition est exprimée en termes des congruences entre les coefficients de Fourier des formes modulaires . On montre comment vérifier ces congruences, et on traite plusieurs...