Over the past few years the understanding of the microscopic theory of black hole entropy has made important conceptual progress by recognizing that the degeneracies are encoded in partition functions which are determined by higher rank automorphic representations, in particular in the context of Siegel modular forms of genus two. In this brief review some of the elements of this framework are ...

We compute the Archimedean doubling zeta integrals which appear in interpolation formulas for p-adic L-functions of Siegel modular forms, and verify that they agree with modified Euler factors conjectured by Coates--Perrin-Riou.

A formula for the exact partition function of 1/4 BPS dyons in a class of CHL models has been proposed earlier. The formula involves inverse of Siegel modular forms of subgroups of Sp(2, ZZ). In this paper we propose product formulae for these modular forms. This generalizes the result of Borcherds and Gritsenko and Nikulin for the weight 10 cusp form of the full Sp(2, ZZ) group.

In our earlier paper [7], we presented an algorithm for computing explicitly the coset representatives and the action of the Hecke operators on Siegel modular forms for arbitrary degree. The action was expressed in terms of the effect on the lattice-Fourier coefficients of the form (see the introduction for a definition of this term). This expression involved combinatorial terms that count loca...

We study the distribution, in the space of Satake parameters, of local components of Siegel cusp forms of genus 2 and growing weight k, subject to a specific weighting which allows us to apply results concerning Bessel models and a variant of Petersson’s formula. We obtain for this family a quantitative local equidistribution result, and derive a number of consequences. In particular, we show t...

We consider four-parameter D = 4, N = 2 string models with Hodge numbers (4, 214 − 12n) and (4, 148), and we express their perturbative Wilsonian gravitational coupling F1 in terms of Siegel modular forms.

We give a precise determination of the algebraicity critical values L -functions associated to Siegel modular forms half-integral weight and arbitrary degree. generalise improve on similar results for integral-weight case by adapting Rankin-Selberg method this setting, with aid Shimura's theory recent work Bouganis. An essential ingredient is proof new analogue Garrett's conjecture Klingen Eise...

In this paper, we revisit the theory of Brandt matrices for algebraic modular forms. We then apply this to the computation of Hilbert-Siegel modular forms of genus 2 over totally real number fields of narrow class number one. Some numerical examples of eigensystems of Hilbert-Siegel modular forms of genus 2 over Q( √ 2) are provided. Introduction Let G/Q be a connected reductive group such that...