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.
The Dimension of the Spaces of Cusp Forms on Siegel Upper Half Plane of Degree Two.
The first negative Hecke eigenvalue of a Siegel cusp form of genus two
The fundamental lemma of a relative trace formula for
The Kodaira dimension of certain moduli spaces of abelian surfaces
The Maaß Space and Hecke Operators.
The Picard group of Siegel modular threefolds.
The universal periods of curves and the Schottky problem
Theta functions of quadratic forms over imaginary quadratic fields
1. Introduction. Let Q be a positive definite n × n matrix with integral entries and even diagonal entries. It is well known that the theta function , Im z > 0, is a modular form of weight n/2 on , where N is the level of Q, i.e. is integral and has even diagonal entries. This was proved by Schoeneberg [5] for even n and by Pfetzer [3] for odd n. Shimura [6] uses the Poisson summation formula to generalize their results for arbitrary n and he also computes the theta multiplier explicitly....
Thetanullwerte and stable modular forms for Hecke groups.
Theta-transforms and even zeta functions of Siegel modular forms
Über das Verhalten von ... und ähnlichen Funktionen bei Modulsubstitutionen.
Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen II.
Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen.
Über die Fourrierkoeffizienten des Siegelschen Eisensteinreihen.