Properties of Lerch Sums and Ramanujan's Mock Theta Functions

Abstract

In this article we study properties of Ramanujan's mock theta functions that can be expressed in Lerch sums. We mainly show that each Lerch sum is actually the integral of a Jacobian theta function (here we show that for ${\vartheta }_3(t,q)$ and ${\vartheta }_4(t,q)$) and the $\sec -$function. We also prove some modular relations and evaluate the Fourier coefficients of a class of Lerch sums.

Mock theta functions

References in corpus (3)

• Mock Theta Functions
• Multivariate Quadratic Transformations and the Interpolation Kernel
• On the Complete Evaluation of Jacobi Theta Functions