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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

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