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claims made by S. Ramanujan in The Lost Notebook and Other Unpublished Papers …

[I] ntuition comes to us much earlier and with much less outside influence than formal
arguments which we cannot really understand unless we have reached a relatively high …

A bstract We find and propose an explanation for a large variety of modularity-related
symmetries in problems of 3-manifold topology and physics of 3d\(\mathcal {N}\)= 2 theories …

One of the most romantic stories in the history of mathematics is that of the friendship
between Hardy and Ramanujan. It began and ended with two famous letters. The first, sent …

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 …

Together with his collaborators, most notably Kathrin Bringmann and Jan Bruinier, the
author has been researching harmonic Maass forms. These non-holomorphic modular forms …

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 …