On a correspondence between p-adic Siegel-Eisenstein series and genus theta series
On Certain Vector Valued Siegel Modular Forms of Degree Two.
On classical weight one forms in Hida families
We give precise estimates for the number of classical weight one specializations of a non-CM family of ordinary cuspidal eigenforms. We also provide examples to show how uniqueness fails with respect to membership of weight one forms in families.
On Congruence Divisors of Cusp Forms as Factors of Special Values of Their Zeta Functions.
On congruence modules associated to -adic forms
On Fourier coefficients of modular forms of different weights
On Galois representations associated to Hilbert modular forms.
On ordinary ...-adic representations associated to modular forms.
On -adic analytic families of Galois representations
On -adic -functions of over totally real fields
Let be the Rankin product -function for two Hilbert cusp forms and . This -function is in fact the standard -function of an automorphic representation of the algebraic group defined over a totally real field. Under the ordinarity assumption at a given prime for and , we shall construct a -adic analytic function of several variables which interpolates the algebraic part of for critical integers , regarding all the ingredients , and as variables.
On p-adic Siegel modular forms of non-real Nebentypus
On Ramanujan congruences between special values of Hecke and Dirichlet L-functions
On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields
Let be a modular elliptic curve defined over a totally real number field and let be its associated eigenform. This paper presents a new method, inspired by a recent work of Bertolini and Darmon, to control the rank of over suitable quadratic imaginary extensions . In particular, this argument can also be applied to the cases not covered by the work of Kolyvagin and Logachëv, that is, when is even and not new at any prime.
On the characteristic power series of the U operator
We show that the coefficients of the characteristic power series of Atkin’s U operator acting on overconvergent -adic modular forms of weight vary -adically continuously as functions of . Are they in fact Iwasawa functions of ?
On the critical values of certain Dirichlet series and the periods of automorphic forms.
On the distribution of analytic values on quadratic twists of elliptic curves.
On the Fourier coefficients of modular forms. II.
On the infinite fern of Galois representations of unitary type
Let be a CM number field, an odd prime totally split in , and let be the -adic analytic space parameterizing the isomorphism classes of -dimensional semisimple -adic representations of satisfying a selfduality condition “of type ”. We study an analogue of the infinite fern of Gouvêa-Mazur in this context and show that each irreducible component of the Zariski-closure of the modular points in has dimension at least . As important steps, and in any rank, we prove that any first order...
On the local behaviour of ordinary -adic representations
Let be a primitive cusp form of weight at least 2, and let be the -adic Galois representation attached to . If is -ordinary, then it is known that the restriction of to a decomposition group at is “upper triangular”. If in addition has CM, then this representation is even “diagonal”. In this paper we provide evidence for the converse. More precisely, we show that the local Galois representation is not diagonal, for all except possibly finitely many of the arithmetic members of a non-CM...
On the non-existence of simple congruences for quotients of Eisenstein series