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Euler-like recurrences for smallest parts functions

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Abstract

We obtain recurrences for smallest parts functions which resemble Euler’s recurrence for the ordinary partition function. The proofs involve the holomorphic projection of non-holomorphic modular forms of weight \(2\).

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Acknowledgments

We thank the referee for comments which improved our exposition.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois, Urbana, IL, 61801, USA

    Scott Ahlgren & Nickolas Andersen

Authors
  1. Scott Ahlgren
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  2. Nickolas Andersen
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Correspondence to Scott Ahlgren.

Additional information

In memory of Basil Gordon

The first author was supported by a grant from the Simons Foundation (#208525 to Scott Ahlgren).

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Ahlgren, S., Andersen, N. Euler-like recurrences for smallest parts functions. Ramanujan J 36, 237–248 (2015). https://doi.org/10.1007/s11139-014-9580-9

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  • DOI: https://doi.org/10.1007/s11139-014-9580-9

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