The Final Problem : An Account of the Mock Theta Functions

@article{Watson1936TheFP,
  title={The Final Problem : An Account of the Mock Theta Functions},
  author={G. N. Watson},
  journal={Journal of The London Mathematical Society-second Series},
  year={1936},
  volume={11},
  pages={55-80}
}
  • G. N. Watson
  • Published 1936
  • Mathematics
  • Journal of The London Mathematical Society-second Series

Mock and mixed mock modular forms in the lower half-plane

We study mock and mixed mock modular forms in the lower half-plane. In particular, our results apply to Zwegers’ three-variable mock Jacobi form $${\mu(u,v;\tau)}$$μ(u,v;τ), three-variable

Jacobi's triple product, mock theta functions, and the $q$-bracket

In Ramanujan’s final letter to Hardy, he wrote of a strange new class of infinite series he called “mock theta functions”. It turns out all of Ramanujan’s mock theta functions are essentially

Properties of the Appell–Lerch function (I)

A number of equations involving the Appell–Lerch function, $$ \mu $$ μ , are derived. Emphasis is placed on equations which are analogous to certain linear relations which exist between theta

Partial New Mock Theta Functions

By using a simple identity of mine, I have proved sixty identities connecting the mock theta functions of Ramanujan with mock theta functions recently generated by Andrews and Bringmann et al, by

Perspectives on mock modular forms

A Survey of Classical Mock Theta Functions

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

A New Identity Relating Mock Theta Functions with Distinct Orders

S. Ramanujan listed 17 mock theta functions of orders 3, 5 and 7 in his last letter to G. H. Hardy. A mock theta function is a function f (q) for |q| < 1 satisfying the following two conditions: (i)

Representations of mock theta functions

Motivated by the works of Liu, we provide a unified approach to find Appell-Lerch series and Hecke-type series representations for mock theta functions. We establish a number of parameterized

Unearthing the visions of a master: harmonic Maass forms and number theory

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