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Vanishing coefficients and identities concerning Ramanujan’s parameters

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Abstract

In this paper we investigate several infinite products with vanishing Taylor coefficients in arithmetic progressions. These infinite products are closely related to Ramanujan’s parameters introduced in his Lost Notebook. Also, a handful of new identities involving these parameters will be established.

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Acknowledgements

The authors would like to acknowledge Mike Hirschhorn for some helpful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Penn State University, University Park, PA, 16802, USA

    Shane Chern

  2. Center for Applied Mathematics, Tianjin University, Tianjin, 300072, People’s Republic of China

    Dazhao Tang

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  1. Shane Chern
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  2. Dazhao Tang
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Correspondence to Dazhao Tang.

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The second author was supported by the Postdoctoral Science Foundation of China (No. 2019M661005).

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Chern, S., Tang, D. Vanishing coefficients and identities concerning Ramanujan’s parameters. Ramanujan J 57, 1367–1385 (2022). https://doi.org/10.1007/s11139-021-00385-z

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