Combination Of Theta Series Research Articles

Theta series and trace operators for Гn[q

We consider the action of suitable trace operators on non homogeneous theta series that are Siegel modular forms for the principal congruence subgroups of the symplectic group of odd levelq: Гn[q]. This is used for investigating whether modular forms forГn[N], withN|q, which are linear combination of such theta series, can be expressed as combination of theta series that are modular forms with respect toГn[N].

L-functions for Jacobi forms and the basis problem

This paper deals with Jacobi forms Φ on ?×ℂ. The Rankin–Selberg doubling method is employed to study properties of the standard L-function of Hecke–Jacobi eigenforms. It is shown that every analytic Klingen–Jacobi Eisenstein series attached to Φ has a meromorphic continuation on the whole complex plane. Hecke–Jacobi cusp eigenforms of weight k > 4 and k≡ 0 mod 4 can written explicitly as a linear combination of theta series. Finally the basis problem of Jacobi forms of square-free index is solved.

Siegel cusp forms of degree 12k and weight 12k

In this paper we prove the existence of cusp forms relative to the full modular group whose genus is equal to the weight. These cusp forms are linear combination of theta series.

Action of the irregular Hecke operator of index p on the theta-series of a quadratic form

Let F be a positive-definite integral even matrix of even order. For an arbitrary prime number p and natural n one obtains an explicit expression for the image of the theta series of genus n of the matrix F, under the action of an irregular Hecke operator with index p, in the form of a linear combination of theta series.