There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This… Expand

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(q) has an… Expand

A method is developed for obtaining Ramanujan's mock theta functions from ordinary theta functions by performing certain operations on their q‐series expansions. The method is then used to construct… Expand

AbstractLet
$$k = p_1^{a_1 } p_2^{a_2 } \cdot \cdot \cdot p_m^{a_m } $$
be the prime factorization of a positive integer k and let bk(n) denote the number of partitions of a non-negative integer n… Expand

AbstractSchur's partition theorem states that the number of partitions ofn into distinct parts ≡ 1,2 (mod 3) is equal to the number of partitions ofn into parts with minimal difference 3 and no… Expand