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### Mahadeva Naika, M. S.

*P-Q* Eta-Function Identities and Computation of Ramanujan-Weber Class Invariants

*P-Q*Eta-Function Identities and Computation of Ramanujan-Weber Class Invariants
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1 Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore-570006, IN

#### Authors

M. S. Mahadeva Naika

^{1}**Affiliations**

1 Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore-570006, IN

#### Source

The Journal of the Indian Mathematical Society, Vol 70, No 1-4 (2003), Pagination: 121-134#### Abstract

In his ‘lost’ notebook, Ramanujan recorded several*P-Q*identities. In this paper we obtain some new

*P-Q*eta-function identities akin to Ramanujan’s and employ them to compute some new values for Ramanujan-Weber class invariant.

#### Keywords

Eta-Function Identities, Class Invariants, Theta-Functions.- Congruences for Overpartition Pairs with Restricted Odd Differences

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#### Authors

#### Source

The Journal of the Indian Mathematical Society, Vol 89, No 3-4 (2022), Pagination: 353-371#### Abstract

Let b^{-(k)} (n) denote the number of overpartition pairs of n where (i) consecutive parts di?er by a multiple of k + 1 unless the larger of the two is overlined, and (ii) the smallest part is overlined unless it is divisible by k+1. We prove many in?nite families of congruences modulo powers of 2 and 3 for b^{-(2)} (n) and congruences modulo 4 and 5 for b^{-(4)} (n). For example, for all n ? 0 and ?,? ? 0,

b^{-(4)}(4·3^{4?} ·5^{2?}(5n + i) + 3^{4?} ·5^{2?})? 0 (mod 5),

where i = 3,4.

#### Keywords

Congruences, Overpartitions, Restricted Odd Differences.#### References

- C. Adiga, B. C. Berndt, S. Bhargava and G. N. Watson, Chapter 16 of Ramanujan’s Second Notebook:Theta functions and q-series, Mem. Amer. Math. Soc., 315 (1985), 1–91.
- N. D. Baruah and K. K. Ojah, Partitions with designated summands in which all parts are odd, Integers, 15 (2015), #A9.
- B. C. Berndt, Ramanujan’s Notebooks Part III, Springer-Verlag, New York, 1991.
- K. Bringmann, J. Dousse, J. Lovejoy and K. Mahlburg, Overpartitions with restricted odd di?erences, Electron. J. Combin., 22 (3) (2015), #P.3.17.
- S. Chern and L. J. Hao, Congruences for two restricted overpartitions, Proc. Indian Acad. Sci. (Math. Sci.), (2019), 129:31.
- M. D. Hirschhorn, The Power of q, Springer International Publishing, Switzerland, 2017.
- M. D. Hirschhorn and J. A. Sellers, Elementary proofs of parity results for 5-regular partitions, Bull. Aust. Math. Soc., 81 (2010), 58–63.
- M. D. Hirschhorn and J. A. Sellers, Arithmetic properties of partitions with odd distinct, Ramanujan J., 22 (2010), 273–284.
- M. D. Hirschhorn and J. A. Sellers, Congruences for overpartitions with restricted odd di?erences, Ramanujan J., 53 (2020), 167–180.
- M. S. Mahadeva Naika and D. S. Gireesh, Congruences for overpartitions with restricted odd di?erences, Afr. Mat., 30 (2019), 1–21.
- S. Ramanujan, Collected Papers, Cambridge University Press, 1927; reprinted by Chelsea, New York, 1962; reprinted by the American Mathematical Society, RI, 2000.
- P. C. Toh, Ramanujan type identities and congruences for partition pairs, Discrete Math., 312 (2012), 1244–1250.