# Congruences modulo powers of 5 for the rank parity function

@article{Chen2021CongruencesMP, title={Congruences modulo powers of 5 for the rank parity function}, author={Dandan Chen and Rong Chen and Frank G. Garvan}, journal={Hardy-Ramanujan Journal}, year={2021} }

International audience
It is well known that Ramanujan conjectured congruences modulo powers of 5, 7 and 11 for the partition function. These were subsequently proved by Watson (1938) and Atkin (1967). In 2009 Choi, Kang, and Lovejoy proved congruences modulo powers of 5 for the crank parity function. The generating function for the rank parity function is f (q), which is the first example of a mock theta function that Ramanujan mentioned in his last letter to Hardy. We prove congruences…

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## References

SHOWING 1-10 OF 31 REFERENCES

### A simple proof of the Ramanujan conjecture for powers of 5.

- Mathematics
- 1981

Ramanujan conjectured, and G. N. Watson proved, that if n is of a specific form then p (n), the number of partitions of «, is divisible by a high power of 5. In the present note, we establish…

### THE f(q) MOCK THETA FUNCTION CONJECTURE AND PARTITION RANKS

- Mathematics
- 2005

In 1944, Freeman Dyson initiated the study of ranks of integer partitions. Here we solve the classical problem of obtaining formulas for Ne(n) (resp. No(n)), the number of partitions of n with even…

### CONGRUENCES INVOLVING F-PARTITION FUNCTIONS

- Mathematics
- 1994

The primary goal of this note is to prove the congruence ϕ 3 ( 3 n + 2 ) ≡ 0 ( mod 3 ) , where ϕ 3 ( n ) denotes the number of F -partitions of n with at most 3 repetitions. Secondarily, we…

### A Proof of some identities of Ramanujan using modular forms

- MathematicsGlasgow Mathematical Journal
- 1989

In 1974 B. J. Birch [1] published a description of some manuscripts of Ramanujan which contained, among other things, a list of forty identities involving the Rogers-Ramanujan functions At that time…

### Automatic Proof of Theta-Function Identities

- MathematicsTexts & Monographs in Symbolic Computation
- 2019

This is a tutorial for using two new MAPLE packages, thetaids and ramarobinsids. The thetaids package is designed for proving generalized eta-product identities using the valence formula for modular…

### On Rationally Parametrized Modular Equations

- Mathematics
- 2006

Many rationally parametrized elliptic modular equations are derived. Each comes from a family of elliptic curves attached to a genus-zero congruence subgroup $\Gamma_0(N)$, as an algebraic…