Estimates for eigenvalues of Hecke operators on Siegel cusp forms.
Estimates for Fourier coefficients of Siegel cusp forms.
Estimates for Fourier coefficients of Siegel cusp forms of degree two
Estimées pour les valuations -adiques des valeurs propres des opérateurs de Hecke
Pour les formes automorphes cuspidales sur les corps de fonctions et pour les formes automorphes cuspidales cohomologiques sur les corps de nombres, on donne des estimées pour les valuations -adiques des valeurs propres des opérateurs de Hecke. Dans le cas des corps de nombres, ces estimées correspondent aux estimées de Katz-Mazur par les conjectures de Langlands.
Euler constants for a Fuchsian group of the first kind
Euler products and Fourier coefficients of automorphic forms on symplectic groups.
Euler system for Galois deformations
In this paper, we develop the Euler system theory for Galois deformations. By applying this theory to the Beilinson-Kato Euler system for Hida’s nearly ordinary modular deformations, we prove one of the inequalities predicted by the two-variable Iwasawa main conjecture. Our method of the proof of the Euler system theory is based on non-arithmetic specializations. This gives a new simplified proof of the inequality between the characteristic ideal of the Selmer group of a Galois deformation and the...
Euler systems obtained from congruences between Hilbert modular forms
Évaluation d'une somme arithmétique associée à une forme modulaire non analytique
Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
The convolution sum, [...] ∑(l,m)∈N02αl+βm=nσ(l)σ(m), where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms are used to achieve these evaluations. Since the modular space of level 22 is contained in that of level 44, we almost completely use the basis elements of the modular space of level 44 to carry out the evaluation of the convolution sums for αβ = 22. We then use these convolution sums to determine formulae for the number of representations of a positive integer by...
Evaluation of the sums
The convolution sum is evaluated for and all . This completes the partial evaluation given in the paper of J. G. Huard, Z. M. Ou, B. K. Spearman, K. S. Williams.
Evaluations of the Rogers-Ramanujan continued fraction R(q) by modular equations
Examples of Eigenvalues of Hecke Operators on Siegel Cusp Forms of Degree Two.
Exceptional congruences for powers of the partition function
Exceptional modular form of weight 4 on an exceptional domain contained in C27.
Resnikoff [12] proved that weights of a non trivial singular modular form should be integral multiples of 1/2, 1, 2, 4 for the Siegel, Hermitian, quaternion and exceptional cases, respectively. The θ-functions in the Siegel, Hermitian and quaternion cases provide examples of singular modular forms (Krieg [10]). Shimura [15] obtained a modular form of half-integral weight by analytically continuing an Eisenstein series. Bump and Bailey suggested the possibility of applying an analogue of Shimura's...
Existence of nonelliptic mod Galois representations for every .
Exotic approximate identities and Maass forms
We obtain some approximate identities whose accuracy depends on the bottom of the discrete spectrum of the Laplace-Beltrami operator in the automorphic setting and on the symmetries of the corresponding Maass wave forms. From the geometric point of view, the underlying Riemann surfaces are classical modular curves and Shimura curves.
Experimental indications of three-dimensional Galois representations from the cohomology of .
Explicit computations of Hilbert modular forms on .
Explicit determination of the images of the Galois representations attached to abelian surfaces with .