Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2019.02.15
  • Accepted : 2019.04.24
  • Published : 2020.03.01
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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.

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Acknowledgement

Supported by : Department of Atomic Energy, Government of India

We are very grateful to Professor Michael Hirschhorn for careful reading of a draft of the manuscript. We thank the referee for the comments. The first author acknowledges the financial support of SERB, Department of Science and Technology, Government of India. The third author acknowledges the financial support of Department of Atomic Energy, Government of India for supporting a part of this work under NBHM Fellowship.

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