## 10 Citations

A mock theta function identity related to the partition rank modulo 3 and 9

- Mathematics, Computer Science
- 2020

A new mock theta function identity related to the partition rank modulo 3 and 9 is proved and the dissection of the rank generating function modulo [Formula: see text] is obtained.

Ranks, cranks for overpartitions and Appell–Lerch sums

- MathematicsThe Ramanujan Journal
- 2021

The definitions of the rank and crank for overpartitions were given by Bringmann, Lovejoy and Osburn. Let $$\overline{N}(s,l;n)$$ N ¯ ( s , l ; n ) (resp. $$\overline{M}(s,l;n)$$ M ¯ ( s , l ; n ) ,…

FOUR IDENTITIES FOR THIRD ORDER MOCK THETA FUNCTIONS

- MathematicsNagoya Mathematical Journal
- 2018

In 2005, using a famous lemma of Atkin and Swinnerton-Dyer (Some properties of partitions, Proc. Lond. Math. Soc. (3) 4 (1954), 84–106), Yesilyurt (Four identities related to third order mock theta…

Arithmetic properties of odd ranks and k-marked odd Durfee symbols

- MathematicsAdv. Appl. Math.
- 2020

Four identities related to third-order mock theta functions

- MathematicsThe Ramanujan Journal
- 2020

Ramanujan presented four identities for third order mock theta functions in his Lost Notebook. In 2005, with the aid of complex analysis, Yesilyurt first proved these four identities. Recently,…

Recent Work on Mock Theta Functions

- Mathematics
- 2018

The work of Ramanujan has had a wide ranging impact in many branches of mathematics. Among many fields of research influenced by Ramanujan, few are as currently vibratingly active as the area of mock…

On three identities of Ramanujan

- Mathematics
- 2021

In this paper, we represent the generating function of the rank function as a summation of four parts—a constant, two Lambert series and a product. Applying it to three of Ramanujan’s identities we…

Identities, inequalities and congruences for odd ranks and k-marked odd Durfee symbols

- MathematicsAdv. Appl. Math.
- 2022

Identities and inequalities for the $$M_2$$-rank of partitions without repeated odd parts modulo 8

- MathematicsThe Ramanujan Journal
- 2021

In 2002, Berkovich and Garvan introduced the $$M_2$$
-rank of partitions without repeated odd parts. Let $$N_2(a, M, n)$$
denote the number of partitions of n without repeated odd parts in which…

Tenth Order Mock Theta Functions: Part III, Identities for χ 10 ( q ), X 10 ( q )

- Mathematics
- 2018

The previous chapter provided an account of S. Zwegers’ ingenious proofs of the first four identities that appear on page 9 of Ramanujan’s Lost Notebook [232]. Identities (5) and (6) have not yielded…

## References

SHOWING 1-10 OF 15 REFERENCES

The generating functions of the rank and crank modulo 8

- Mathematics
- 2009

Abstract
Let N(i,m;n) be the number of partitions of n with rank (Dyson) congruent to i (mod m) and let M(j,m;n) be the number of partitions of n with crank (Andrews, Garvan) congruent to j (mod m).…

Dyson’s ranks and Appell–Lerch sums

- Mathematics
- 2013

Denote by p(n) the number of partitions of n and by N(a, M; n) the number of partitions of n with rank congruent to a modulo M. We find and prove a general formula for Dyson’s ranks by considering…

Dyson's crank of a partition

- Mathematics
- 1988

holds. He was thus led to conjecture the existence of some other partition statistic (which he called the crank); this unknown statistic should provide a combinatorial interpretation of ^-p(lln + 6)…

On the rank and the crank modulo 4 and 8

- Mathematics
- 1994

In this paper we prove some identities, conjectured by Lewis, for the rank and crank of partitions concerning the modulo 4 and 8. These identities are similar to Dyson's identities for the rank…

FOUR IDENTITIES FOR THIRD ORDER MOCK THETA FUNCTIONS

- MathematicsNagoya Mathematical Journal
- 2018

In 2005, using a famous lemma of Atkin and Swinnerton-Dyer (Some properties of partitions, Proc. Lond. Math. Soc. (3) 4 (1954), 84–106), Yesilyurt (Four identities related to third order mock theta…

Ramanujan's Lost Notebook: Part I

- Mathematics
- 2005

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews…

Hecke‐type double sums, Appell–Lerch sums, and mock theta functions, I

- Mathematics
- 2014

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 sums. Not only does our…

On three third order mock theta functions and Hecke-type double sums

- Mathematics
- 2013

We obtain four Hecke-type double sums for three of Ramanujan’s third order mock theta functions. We discuss how these four are related to the new mock theta functions of Andrews’ work on q-orthogonal…