Modular forms of orthogonal type and Jacobi theta-series

DOI10.1007/s12188-013-0080-4zbMath1355.11053arXiv1106.4733OpenAlexW2007854534MaRDI QIDQ376734

Fabien Cléry, Valery Gritsenko

Publication date: 19 November 2013

Published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.4733

zbMATH Keywords

Jacobi forms for lattices and root systemslifting of modular formsmodular forms of orthogonal typetheta-series and Weil representations

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Other groups and their modular and automorphic forms (several variables) (11F55) Jacobi forms (11F50)

Related Items (19)

Modular forms. Abstracts from the workshop held April 27 -- May 3, 2014. ⋮ The \(D_8\)-tower of weak Jacobi forms and applications ⋮ Conjecture on theta-blocks of order 1 ⋮ Graded rings of integral Jacobi forms ⋮ Elliptic genus and modular differential equations ⋮ Modular differential equations of the elliptic genus of Calabi-Yau fourfolds ⋮ On some free algebras of orthogonal modular forms ⋮ The classification of 2-reflective modular forms ⋮ Weight one Jacobi forms and umbral moonshine ⋮ Modular forms for the \(A_1\)-tower ⋮ Borcherds products everywhere ⋮ The structure of the algebra of weak Jacobi forms for the root system \(F_4\) ⋮ Powers of Jacobi triple product, Cohen's numbers and the Ramanujan \(\Delta\)-function ⋮ Jacobi forms of higher index and paramodular groups in \( \mathcal{N} = 2\), \(D= 4\) compactifications of string theory ⋮ On some free algebras of orthogonal modular forms. II ⋮ Antisymmetric paramodular forms of weight 3 ⋮ Theta block conjecture for paramodular forms of weight 2 ⋮ Reflective modular forms and applications ⋮ The classification of free algebras of orthogonal modular forms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Abelianisation of orthogonal groups and the fundamental group of modular varieties
• The theory of Jacobi forms
• Über Kernfunktionen für Jacobiformen und Siegelsche Modulformen. (Kernel functions for Jacobi forms and Siegel modular forms)
• Infinite-dimensional Lie algebras, theta functions and modular forms
• Automorphic forms with singularities on Grassmannians
• Elliptic genera of symmetric products and second quantized strings
• Tata lectures on theta. I: Introduction and motivation: Theta functions in one variable. Basic results on theta functions in several variables. With the assistance of C. Musili, M. Nori, E. Previato, and M. Stillman
• Automorphic forms on \(O_{s+2,2}(\mathbb R)\) and infinite products
• The moduli space of Enriques surfaces and the fake monster Lie superalgebra
• Commutator coverings of Siegel threefolds.
• The arithmetic mirror symmetry and Calabi-Yau manifolds
• The Kodaira dimension of the moduli of \(K3\) surfaces
• Construction of reflective automorphic forms in a four-dimensional space
• On the classification of automorphic products and generalized Kac-Moody algebras
• Siegel modular forms of genus 2 with the simplest divisor
• Some Siegel threefolds with a Calabi-Yau model
• Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebras
• The moduli space of Enriques surfaces and Borcherds products
• Jacobi forms of critical weight and Weil representations
• AUTOMORPHIC FORMS AND LORENTZIAN KAC–MOODY ALGEBRAS PART I
• AUTOMORPHIC FORMS AND LORENTZIAN KAC–MOODY ALGEBRAS PART II

This page was built for publication: Modular forms of orthogonal type and Jacobi theta-series