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Generalized Lambert Series and Euler’s Pentagonal Number Theorem

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Abstract

We consider the number of k’s in all the partitions of n, and provide new connections between partitions and functions from multiplicative number theory. In this context, we obtain a new generalization of Euler’s pentagonal number theorem and provide combinatorial interpretations for some special cases of this general result.

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Acknowledgements

The author wish to thank the anonymous referees for a very careful reading of the original manuscript.

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Authors and Affiliations

  1. Department of Mathematics, University of Craiova, 200585, Craiova, Romania

    Mircea Merca

  2. Academy of Romanian Scientists, Ilfov 3, Sector 5, Bucharest, Romania

    Mircea Merca

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  1. Mircea Merca
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Correspondence to Mircea Merca.

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Merca, M. Generalized Lambert Series and Euler’s Pentagonal Number Theorem. Mediterr. J. Math. 18, 29 (2021). https://doi.org/10.1007/s00009-020-01663-8

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  • DOI: https://doi.org/10.1007/s00009-020-01663-8

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