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We study a certain finitely generated multiplicative subgroup of the Hilbert class field of a quartic CM field. It consists of special values of certain theta functions of genus 2 and is analogous to the group of Siegel units. Questions of integrality of these specials values are related to the arithmetic of the Siegel moduli space.

On the differential of applications defined on moduli spaces of p.p.a.v. with level theata structure.

R. Salvati Manni (1996)

Mathematische Zeitschrift

On the Dimensions of Spaces of Siegel Modular Forms of Weight One.

J.-S. Li (1996)

Geometric and functional analysis

On the Holomorphic Differential Forms of the Siegel Modular Variety II.

Riccardo Salvati Manni (1990)

Mathematische Zeitschrift

On the l-adic cohomology of Siegel threefolds.

Richard Taylor (1993)

Inventiones mathematicae

On the residue of the Eisenstein series and the Siegel-Weil formula

Tamotsu Ikeda (1996)

Compositio Mathematica

On the spezialschar of Maass.

Heim, Bernhard (2010)

International Journal of Mathematics and Mathematical Sciences

On the spinor zeta functions problem: higher power moments of the Riesz mean

Haiyan Wang (2013)

Acta Arithmetica

Let F be a Siegel cusp form of integral weight k on the Siegel modular group Sp₂(ℤ) of genus 2. The coefficients of the spinor zeta function $Z_{F} (s)$ are denoted by cₙ. Let $D_{ρ} (x; Z_{F})$ be the Riesz mean of cₙ. Kohnen and Wang obtained the truncated Voronoï-type formula for $D_{ρ} (x; Z_{F})$ under the Ramanujan-Petersson conjecture. In this paper, we study the higher power moments of $D_{ρ} (x; Z_{F})$ , and then derive an asymptotic formula for the hth (h=3,4,5) power moments of $D ₁ (x; Z_{F})$ by using Ivić’s large value arguments and other techniques.

$p$ -adic measures attached to Siegel modular forms

Siegfried Böcherer, Claus-Günther Schmidt (2000)

Annales de l'institut Fourier

We study the critical values of the complex standard- $L$ -function attached to a holomorphic Siegel modular form and of the twists of the $L$ -function by Dirichlet characters. Our main object is for a fixed rational prime number $p$ to interpolate $p$ -adically the essentially algebraic critical $L$ -values as the Dirichlet character varies thus providing a systematic control of denominators of critical values by generalized Kummer congruences. In order to organize this information we prove the existence of...

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On Poincaré series on Spm.

On Saito-Kurokawa Descent for congruence subgroups.

On Siegel modular forms

On Siegel modular forms. Part I.

On Siegel's Modular Group.

On special values of theta functions of genus two

On the differential of applications defined on moduli spaces of p.p.a.v. with level theata structure.

On the Dimensions of Spaces of Siegel Modular Forms of Weight One.

On the Holomorphic Differential Forms of the Siegel Modular Variety II.

On the l-adic cohomology of Siegel threefolds.

On the residue of the Eisenstein series and the Siegel-Weil formula

On the spezialschar of Maass.

On the spinor zeta functions problem: higher power moments of the Riesz mean

$p$ -adic measures attached to Siegel modular forms

Poles and resiudues of standard L-functions attached to Siegel modular forms.

Several-variable $p$ -adic families of Siegel-Hilbert cusp eigensystems and their Galois representations

Siegel varieties and $p$ -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.

Currently displaying 61 – 80 of 120