Relations for Modular Forms from Vertex Operator Algebras

Abstract

We will give a short reminder for vertex operator algebra notion and corresponding characters. Then we discuss algebraic methods for explicit computation of the partition and correlation functions. We then illustrate general ways to find number theory identities for related modular forms by specific examples of modular form relations arising from our construction. Finally, we present new results concerning identities for prime forms on genus g Riemann surfaces and genus two n-point functions for vertex operator algebra characters.