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http://dx.doi.org/10.4134/JKMS.j190143

CONGRUENCES MODULO POWERS OF 2 FOR OVERPARTITION PAIRS INTO ODD PARTS  

Ahmed, Zakir (Department of Mathematics Barnagar College)
Barman, Rupam (Department of Mathematics Indian Institute of Technology Guwahati)
Ray, Chiranjit (Department of Mathematics Indian Institute of Technology Guwahati)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 471-487 More about this Journal
Abstract
We find congruences modulo 32, 64 and 128 for the partition function ${\overline{PP}_o}(n)$, the number of overpartition pairs of n into odd parts, with the aid of Ramamnujan's theta function identities and some known identities of tk(n), for k = 6, 7, where tk(n) denotes the number of representations of n as a sum of k triangular numbers. We also find two Ramanujan-like congruences for ${\overline{PP}_o}(n)$ modulo 128.
Keywords
Partition; p-dissection; theta function; triangular numbers; congruence;
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