Eisenstein Series Of Degree Research Articles

On Fourier–Jacobi expansions of real analytic Eisenstein series of degree 2

We discuss the Fourier–Jacobi expansion of certain vector valued Eisenstein series of degree $$2$$ , which is also real analytic. We show that its coefficients of index $$\pm 1$$ can be described by using a generating series of real analytic Jacobi forms. We also describe all the coefficients of general indices in suitable manners. Our method can be applied to study another Fourier series of Saito-Kurokawa type that is associated with a cusp form of one variable and half-integral weight. Then, following the arguments in the holomorphic case, we find that the Fourier series indeed defines a real analytic Siegel modular form of degree 2.

A p-ADIC LIMIT OF SIEGEL–EISENSTEIN SERIES OF PRIME LEVEL q

We show that a p-adic limit of a Siegel–Eisenstein series of prime level q becomes a Siegel modular form of level pq. This paper contains a simple formula for Fourier coefficients of a Siegel–Eisenstein series of degree two and prime levels.

On p-adic Siegel–Eisenstein series of weight k

show that this series is a Siegel–Eisenstein series of degree two, weight k and level p. As a corollary it is a modular form. We also present a simple formula for the Fourier coefficients of a Siegel–Eisenstein series ofdegree two and prime levels. Let E (2) be the Siegel–Eisenstein series of degree two, weight k and level one, E (2) (Z) = X {C,D} det(CZ + D) −k , Z ∈ H2,

Eisenstein series on quaternion half-space

Kaufhold [5] calculated the Fourier coefficients of the Siegel's Eisenstein series of degree 2 and obtained its analytic continuation and functional equation. In this paper, we follow his procedure to obtain the analytic continuation and a functional equation of the Eisenstein series on quaternion half-space defined by Krieg [7]. S. Nagaoka has announced a similar result (see below).

On Eisenstein series of degree two

On Eisenstein series of degree two

�ber die Fourierkoeffizienten der Siegelschen Eisensteinreihen

It is well known that the Fourier coefficients a n k (T) of Siegel's Eisenstein series of degree n and weight k are rational numbers with bounded denominators [14], [15]. In this paper we introduce a number b n k (T), which is equal to a n k (T) in many cases. This number can be computed in an elementary way. From our explicit formulas for b n k (T) we can easily get results about the denominators of the Fourier coefficients a n k (T), which are better than those obtained by Siegel in his difficult paper [15].

On Eisenstein series of degree two for Hilbert-Siegel modular groups

On Eisenstein series of degree two for Hilbert-Siegel modular groups

On Fourier coefficients of Klingen's Eisenstein series of degree three

On Fourier coefficients of Klingen's Eisenstein series of degree three

On Eisenstein series of degree two

On Eisenstein series of degree two