Abstract
Let \(pod_3(n)\) denote the number of 3-regular partitions of n with distinct odd parts (and even parts are unrestricted). In this article, we prove an infinite family of congruences for \(pod_3(n)\) using the theory of Hecke eigenforms. We also study the divisibility properties of \(pod_3(n)\) using arithmetic properties of modular forms.
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The authors would like to thank the anonymous reviewer for his her valuable comments and helpful suggestions, which has substantially improved our paper.
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Communicated by Jens Funke.
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The first author’s research is supported by Pondicherry University Fellowship, Puducherry-605014 .
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Veena, V.S., Fathima, S.N. Arithmetic properties of 3-regular partitions with distinct odd parts. Abh. Math. Semin. Univ. Hambg. 91, 69–80 (2021). https://doi.org/10.1007/s12188-021-00230-6
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DOI: https://doi.org/10.1007/s12188-021-00230-6