Interprétation combinatoire des moments négatifs des valeurs de fonctions L au bord de la bande critique
Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes
Let be a cuspidal newform with complex multiplication (CM) and let be an odd prime at which is non-ordinary. We construct admissible -adic -functions for the symmetric powers of , thus verifying conjectures of Dabrowski and Panchishkin in this special case. We combine this with recent work of Benois to prove the trivial zero conjecture in this setting. We also construct “mixed” plus and minus -adic -functions and prove an analogue of Pollack’s decomposition of the admissible -adic -functions....
Jacobi forms and certain special values of Dirichlet series associated to modular form.
Jacobi-Eisenstein series and -adic interpolation of symmetric squares of cusp forms
The aim of this paper is to construct and calculate generating functions connected with special values of symmetric squares of modular forms. The Main Theorem establishes these generating functions to be Jacobi-Eisenstein series i.e. Eisenstein series among Jacobi forms. A theorem on -adic interpolation of the special values of the symmetric square of a -ordinary modular form is proved as a corollary of our Main Theorem.
Koecher-Maass series of a certain half-integral weight modular form related to the Duke-Imamoḡlu-Ikeda lift
Let k and n be positive even integers. For a cuspidal Hecke eigenform h in the Kohnen plus space of weight k - n/2 + 1/2 for Γ₀(4), let f be the corresponding primitive form of weight 2k-n for SL₂(ℤ) under the Shimura correspondence, and Iₙ(h) the Duke-Imamoḡlu-Ikeda lift of h to the space of cusp forms of weight k for Spₙ(ℤ). Moreover, let be the first Fourier-Jacobi coefficient of Iₙ(h), and be the cusp form in the generalized Kohnen plus space of weight k - 1/2 corresponding to under the...
Koecher-Maaß-Series for Modular Forms of Quaternions.
Kummer's Criterion for the Special Values of Hecke L-Functions of Imaginary Quadratic Fields and Congruences Among Cusp Forms.
-functions.
-functions of automorphic forms and combinatorics: Dyck paths
We give a combinatorial interpretation for the positive moments of the values at the edge of the critical strip of the -functions of modular forms of and . We deduce some results about the asymptotics of these moments. We extend this interpretation to the moments twisted by the eigenvalues of Hecke operators.
La conjecture de Birch et Swinnerton-Dyer -adique
La conjecture de Birch et Swinnerton-Dyer prédit que l’ordre du zéro en de la fonction d’une courbe elliptique définie sur est égal au rang du groupe de ses points rationnels. On sait démontrer cette conjecture si ou , mais on n’a aucun résultat reliant et si . Nous expliquerons comment Kato démontre que la fonction -adique attachée à a, en , un...
Le prolongement -adique analytique des fonctions de Rankin
Le système d’Euler de Kato
Ce texte est consacré au système d’Euler de Kato, construit à partir des unités modulaires, et à son image par l’application exponentielle duale (loi de réciprocité explicite de Kato). La présentation que nous en donnons est sensiblement différente de la présentation originelle de Kato.
L-functions and periods of polarized regular motives.
Low lying zeros of families of -functions
L-Series of Rankin Type and Their Functional Equations.
Mahler's measure and special values of -functions.
Mahler's measure: proof of two conjectured formulae.
Metaplectic forms and Gauss sums I
Mixed Hodge structures and automorphic forms for Siegel modular varieties of degree two.
Modular forms and de Rham cohomology; Atkin-Swinnerton-Dyer congruences.