A proof of the mock theta conjectures (Q1112867)

In his ``lost'' notebook, Ramanujan stated identities involving each of the ten fifth order mock theta functions, which he divided into two groups. \textit{G. E. Andrews} and \textit{F. G. Garvan} [Ramanujan's ``Lost'' Notebook VI: The mock theta conjectures; Adv. Math. 73, No.2, 242-255 (1989)] showed that these identities are all equivalent to two identities, which they call the first and second mock theta conjectures (one conjecture for each group of mock theta functions). The author proves both of these conjectures. The proof relies on a pair of Hecke type identities discovered by \textit{G. E. Andrews} [Trans. Am. Math. Soc. 293, 113-134 (1986; Zbl 0593.10018)].