Difference of a hauptmodul for \(\Gamma_0 (N)\) and certain Gross-Zagier type CM value formulas

DOI10.1007/s11425-019-1830-3zbMath1483.14045arXiv1708.08783OpenAlexW3162514282WikidataQ113900265 ScholiaQ113900265MaRDI QIDQ2078983

Dongxi Ye

Publication date: 4 March 2022

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.08783

zbMATH Keywords

Borcherds productGross-Zagier CM value formulamodular forms for Weil representationmonster denominator formula

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Theta series; Weil representation; theta correspondences (11F27) Complex multiplication and moduli of abelian varieties (11G15) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (4)

On a conjecture of Chen and Yui: Resultants and discriminants ⋮ Singular moduli of \(r\)th roots of modular functions ⋮ On the generating function of a canonical basis for \(M_{0}^{!,\infty }(\Gamma)\) ⋮ Twisted Borcherds products associated to genus zero \(\Gamma_0(N)\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algebraic formulas for the coefficients of mock theta functions and Weyl vectors of Borcherds products
• Intersections of Hirzebruch--Zagier divisors and CM cycles
• Algebraic cycles on Shimura varieties of orthogonal type
• Automorphic forms with singularities on Grassmannians
• The theta-operator and the divisors of modular forms on genus zero subgroups
• Reflection groups of Lorentzian lattices
• Gross-Zagier type CM value formulas on \(X_0^\ast(p)\)
• Monstrous moonshine and monstrous Lie superalgebras
• Automorphic forms on \(O_{s+2,2}(\mathbb R)\) and infinite products
• Heegner modules and elliptic curves
• The Gross-Kohnen-Zagier theorem in higher dimensions
• On the generating function of a canonical basis for \(M_{0}^{!,\infty }(\Gamma)\)
• Generalized moonshine. II: Borcherds products
• CM number fields and modular forms
• Some constructions of modular forms for the Weil representation of SL₂(ℤ)
• Special Values of Green Functions at Big CM Points
• Generalized Kac-Moody algebras, automorphic forms and Conway's group II
• Borcherds forms and generalizations of singular moduli
• On the singular values of Weber modular functions
• Difference of modular functions and their CM value factorization
• The Lambda Invariants at CM Points
• On a conjecture of Chen and Yui: Resultants and discriminants

This page was built for publication: Difference of a hauptmodul for \(\Gamma_0 (N)\) and certain Gross-Zagier type CM value formulas