Classical and overconvergent modular forms
Cohomology of arithmetic groups and congruences between systems of Hecke eigenvalues.
Coleman power series for and -adic zeta functions of modular forms.
Companion forms and weight one forms.
Computation of -adic heights and log convergence.
Congruence modules related to Eisenstein series
Congruence Properties and Density Problems for the Fourier Coefficients of Modular Forms.
Congruence properties of the hyperkloosterman sum
Congruences among modular forms on U(2,2) and the Bloch-Kato conjecture
Let be a positive integer divisible by 4, a prime, an elliptic cuspidal eigenform (ordinary at ) of weight , level 4 and non-trivial character. In this paper we provide evidence for the Bloch-Kato conjecture for the motives and , where is the motif attached to . More precisely, we prove that under certain conditions the -adic valuation of the algebraic part of the symmetric square -function of evaluated at provides a lower bound for the -adic valuation of the order of the Pontryagin...
Congruences between cusp forms and the geometry of Jacobians of modular curves.
Congruences between modular forms and lowering the level mod
In this article we study the behavior of inertia groups for modular Galois mod representations and in some cases we give a generalization of Ribet’s lowering the level result (cf. [9]).
Congruences between Siegel modular forms on the level of group cohomology
Vector-valued Siegel modular forms may be found in certain cohomology groups with coefficients lying in an irreducible representation of the symplectic group. Using functoriality in the coefficients, we show that the ordinary components of the cohomology are independent of the weight parameter. The meaning of ordinary depends on a choice of parabolic subgroup of , giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible...
Congruences for Eigenvalues of Hecke Operators on Siegel Modular Forms of Degree Two.
Congruences for Eigenvalues of Hecke Operators on SL2(Z).
Congruences for Siegel modular forms
We employ recent results on Jacobi forms to investigate congruences and filtrations of Siegel modular forms of degree . In particular, we determine when an analog of Atkin’s -operator applied to a Siegel modular form of degree is nonzero modulo a prime . Furthermore, we discuss explicit examples to illustrate our results.
Construction of eigenvarieties in small cohomological dimensions for semi-simple, simply connected groups.
Control theorems of -nearly ordinary cohomology groups for
Cuspidal groups, ordinary Eisenstein series, and Kubota-Leopoldt p-adic L-functions