Several-variable -adic families of Siegel-Hilbert cusp eigensystems and their Galois representations
Siegel varieties and -adic Siegel modular forms.
Siegel's Modular Forms and the Arithmetic of Quadratic Forms.
Some congruence property of modular forms.
Some properties of Fourier coefficients of Eisenstein series of degree two.
Some remarks on the moduli space of principally polarized abelian varieties with level -structure
Special values of the standard zeta functions for elliptic modular forms.
Sturm type theorem for Siegel modular forms of genus 2 modulo p
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.
Sur la théorie de Hida pour le groupe
Nous construisons des familles ordinaires -adiques de formes modulaires pour le groupe . Notre travail généralise et précise des travaux antérieurs de Hida.
Surjectivity of Siegel -operator for square free level and small weight
We show the surjectivity of the (global) Siegel -operator for modular forms for certain congruence subgroups of and weight , where the standard techniques (Poincaré series or Klingen-Eisenstein series) are no longer available. Our main tools are theta series and genus versions of basis problems.
Symplectic periods.