The Siegel modular forms of genus 2 with the simplest divisor

Abstract

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 question formulated during the conference "Black holes, Black Rings and Modular Forms" (ENS, Paris, August 2007). These modular forms generalize the classical Igusa form and the forms constructed by Gritsenko and Nikulin in 1998.

References in corpus (3)

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• Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift
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• Reflective modular forms in algebraic geometry
• Unravelling Mathieu Moonshine
• Generalised Mathieu Moonshine
• BKM Lie superalgebras from counting twisted CHL dyons -- II
• Weight One Jacobi Forms and Umbral Moonshine
• Brewing moonshine for Mathieu
• Second Quantized Mathieu Moonshine
• Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian Borcherds Algebras
• Powers of Jacobi triple product, Cohen's numbers and the Ramanujan $\Delta$-function
• Computing Borcherds Products
• Automorphic Black Holes as Probes of Extra Dimensions
• Twisted elliptic genus for K3 and Borcherds product
• Two moonshines for $L_2(11)$ but none for $M_{12}$
• Positivity of discrete information for CHL black holes
• Mathieu Moonshine and Siegel Modular Forms
• Some comments on symmetric orbifolds of K3
• Reflective modular forms: A Jacobi forms approach
• $\widehat{sl(2)}$ decomposition of denominator formulae of some BKM Lie superalgebras
• Reflective modular forms on lattices of prime level
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model
• Borcherds Products Everywhere
• Mock Modularity Of Twisted Index In CHL Models
• Sums of four polygonal numbers: precise formulas
• $\widehat{sl(2)}$ decomposition of denominator formulae of some BKM Lie superalgebras -- II