## 137 Citations

Several new product identities in relation to two-variable Rogers-Ramanujan type sums and mock theta functions

- Mathematics
- 2020

Product identities in two variables $x, q$ expand infinite products as infinite sums, which are linear combinations of theta functions; famous examples include Jacobi's triple product identity,…

Universal mock theta functions and two-variable Hecke–Rogers identities

- Mathematics
- 2014

We obtain two-variable Hecke–Rogers identities for three universal mock theta functions. This implies that many of Ramanujan’s mock theta functions, including all the third-order functions, have a…

Overpartitions and class numbers of binary quadratic forms

- MathematicsProceedings of the National Academy of Sciences
- 2009

We show that the Zagier–Eisenstein series shares its nonholomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a…

Dyson’s rank, overpartitions, and universal mock theta functions

- MathematicsCanadian Mathematical Bulletin
- 2020

Abstract In this paper, we decompose
$\overline {D}(a,M)$
into modular and mock modular parts, so that it gives as a straightforward consequencethe celebrated results of Bringmann and Lovejoy on…

Transformation properties for Dyson’s rank function

- MathematicsTransactions of the American Mathematical Society
- 2018

At the 1987 Ramanujan Centenary meeting Dyson asked for a coherent group-theoretical structure for Ramanujan's mock theta functions analogous to Hecke's theory of modular forms. Many of Ramanujan's…

Eulerian series as Modular forms revisited

- Mathematics
- 2015

Recently, Bringmann, Ono, and Rhoades employed harmonic weak Maass forms to prove results on Eulerian series as modular forms. By changing the setting to Appell--Lerch sums, we shorten the proof of…

A partition identity and the universal mock theta function $g_2$

- Mathematics
- 2013

We prove analytic and combinatorial identities reminiscent of Schur's classical partition theorem. Specifically, we show that certain families of overpartitions whose parts satisfy gap conditions are…

The H and K Family of Mock Theta Functions

- MathematicsCanadian Journal of Mathematics
- 2012

Abstract In his last letter to Hardy, Ramanujan defined 17 functions $F\left( q \right),\,\left| q \right|\,<\,1$ , which he called mock $\theta $ -functions. He observed that as $q$ radially…

Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions

- Mathematics
- 2003

In his last letter to Hardy, Ramanujan defined 17 functions F(q), where |q| < 1. He called them mock theta functions, because as q radially approaches any point e2πir (r rational), there is a theta…

ON THE TENTH-ORDER MOCK THETA FUNCTIONS

- MathematicsJournal of the Australian Mathematical Society
- 2017

Using properties of Appell–Lerch functions, we give insightful proofs for six of Ramanujan’s identities for the tenth-order mock theta functions.

## References

SHOWING 1-10 OF 12 REFERENCES

A simple proof of Ramanujan’s summation of the1ψ1

- Mathematics
- 1978

A simple proof by functional equations is given for Ramanujan’s1ψ1 sum. Ramanujan’s sum is a useful extension of Jacobi's triple product formula, and has recently become important in the treatment of…

Applications of Basic Hypergeometric Functions

- Mathematics
- 1974

This paper surveys recent applications of basic hypergeometric functions to partitions, number theory, finite vector spaces, combinatorial identities and physics.

An Introduction to the Theory of Numbers

- Philosophy
- 1938

This is the fifth edition of a work (first published in 1938) which has become the standard introduction to the subject. The book has grown out of lectures delivered by the authors at Oxford,…