This is the fifth and final volume that the authors have written in their examination of all the
claims made by S. Ramanujan in The Lost Notebook and Other Unpublished Papers …

Monstrous moonshine relates distinguished modular functions to the representation theory
of the Monster. The celebrated observations that 1= 1, 196884= 1+ 196883, 21493760= 1+ …

Mock modular forms have found applications in numerous branches of mathematical
sciences since they were first introduced by Ramanujan nearly a century ago. In this …

A partition of a positive integer n is any nonincreasing sequence of p itive integers whose
sum is n. Let p (n) denote the number of partitions o (as usual, we adopt the convention that …

We describe surprising relationships between automorphic forms of various kinds, imaginary
quadratic number fields and a certain system of six finite groups that are parameterised …

By introducing a dual notion between partial theta functions and Appell–Lerch sums, we find
and prove a formula which expresses Hecke-type double sums in terms of Appell–Lerch …

In his last letter to Hardy, Ramanujan defined 17 functions M (q),| q|< 1, which he called
mock θ-functions. He observed that as q radially approaches any root of unity ζ at which M …

Recent works, mostly related to Ramanujan's mock theta functions, make use of the fact that
harmonic weak Maass forms can be combinatorial generating functions. Generalizing works …

In this paper we construct certain mock modular forms of weight 1/2 whose Fourier
coefficients are given in terms of cycle integrals of the modular j-function. Their shadows are …

Abstract The Umbral Moonshine Conjectures assert that there are infinite-dimensional
graded modules, for prescribed finite groups, whose McKay–Thompson series are certain …