Saito-Kurokawa Lifts, L-values for GL2, and Congruences Between Siegel ModularForms

We prove that there exist exactly eight Siegel modular forms with respect to the congruence subgroups of Hecke type of the paramodular groups of genus two vanishing precisely along the diagonal of the Siegel upper half-plane. This is a solution of a problem formulated during the conference “Black holes, Black Rings and Modular Forms” (ENS, Paris, August 2007). These modular forms generalize the...

For $g=8,12,16$ and $24$, there is a nonzero alternating $g$-multilinear form on the ${\\rm Leech}$ lattice, unique up to scalar, which invariant by orthogonal group of Leech}$. The harmonic Siegel theta series built from these forms are modular cuspforms weight $13$ for Sp}{2g}(\\mathbb{Z})$. We prove that they eigenforms, determine one their Fourier coefficients, give informations about stand...

We study the L-functions associated to Siegel modular forms — equivalently, automorphic representations of GSp(4, ‫ށ‬ ‫ޑ‬) — both theoretically and numerically. For the L-functions of degrees 10, 14, and 16 we perform representation theoretic calculations to cast the Langlands L-function in classical terms. We develop a precise notion of what it means to test a conjectured functional equation f...