Applications of CFT determinant formulas in number theory

2025/08/02 by Levin, D., Shin, H. -G., Zuevsky, A.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2508.01301

Abstract

In this note we show how to use the determinant representations for correlation functions in CFT to derive new determinant formulas for powers of the modular discriminant expressed via deformed elliptic functions with parameters. In particular, we obtain counterparts of Garvan's formulas for the modular discriminant corresponding to the genus two Riemann surface case.

Citations

• Genus g Zhu Recursion for Vertex Operator Algebras and Their Modules
• Effect of interactions on the topological expression for the chiral separation effect
• Momentum space topology of QCD
• Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras II
• Hankel determinants of Eisenstein series

Related

• Note on the Tau Function
• Discriminants of cubic curves and determinantal representations
• Hankel determinants of Eisenstein series
• Algebraic twists of modular forms and Hecke orbits
• Frobenius determinants and Bessel Functions