On the Spezialschar of Maass

Abstract

Sym 2 M k+2ν is given. This leads to a basic characterization of the Spezialschar property. The results of this paper are directly related to the non-vanishing of certain special values of L-functions related to the Gross-Prasad conjecture. This is illustrated by a significant example in the paper.

Separators of Siegel modular forms of degree two

“…It is built on the restricted modified derivatives of the Siegel form and on a sharp result for a principal separator of elliptic forms. The first ingredient is at the moment only available for level one [4], since questions on new and old Siegel modular forms and on the number of derivatives needed to determine the form are delicate. As pointed out by the referee, the second ingredient can be given in a much more general form.…”

Hecke duality of Ikeda lifts

“…For Siegel modular forms of degree 2 we obtain sharper results. Moreover, a combination of these results with [12] leads to converse theorems. Finally, we use differential operators to apply pullbacks of Ikeda lifts.…”

Congruences for the Ramanujan function and generalized class numbers

“…Moreover, it follows from the definition that all Fourier coefficients are integers. Since {2, 3,5,7,23, 691} is the set of all exceptional primes related to l-adic Galois representations of ∆ we can apply the theorem for the case m 1 = 131 and 593.…”

“…It follows from [7] that α = 0 and β = 0, since Siegel type Eisenstein series are elements of the Maass Spezialschar and there are no elliptic cusp forms of weight 14. Moreover, it is obvious that β is a rational number.…”