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The saddle-point method for general partition functions

Gregory Debruyne (UGent) and Gérald Tenenbaum
(2020) INDAGATIONES MATHEMATICAE-NEW SERIES. 31(4). p.728-738
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Abstract
We apply the saddle-point method to derive asymptotic estimates or asymptotic series for the number of partitions of a natural integer into parts chosen from a subset of the positive integers whose associated Dirichlet series satisfies certain analytic properties. This enables grouping in a single statement many cases studied in the literature, as well as a number of new ones. (C) 2020 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
Keywords
Partitions, Saddle-point method, Asymptotic formula, Abstract partitions

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Citation

Please use this url to cite or link to this publication:

MLA
Debruyne, Gregory, and Gérald Tenenbaum. “The Saddle-Point Method for General Partition Functions.” INDAGATIONES MATHEMATICAE-NEW SERIES, vol. 31, no. 4, 2020, pp. 728–38, doi:10.1016/j.indag.2020.06.010.
APA
Debruyne, G., & Tenenbaum, G. (2020). The saddle-point method for general partition functions. INDAGATIONES MATHEMATICAE-NEW SERIES, 31(4), 728–738. https://doi.org/10.1016/j.indag.2020.06.010
Chicago author-date
Debruyne, Gregory, and Gérald Tenenbaum. 2020. “The Saddle-Point Method for General Partition Functions.” INDAGATIONES MATHEMATICAE-NEW SERIES 31 (4): 728–38. https://doi.org/10.1016/j.indag.2020.06.010.
Chicago author-date (all authors)
Debruyne, Gregory, and Gérald Tenenbaum. 2020. “The Saddle-Point Method for General Partition Functions.” INDAGATIONES MATHEMATICAE-NEW SERIES 31 (4): 728–738. doi:10.1016/j.indag.2020.06.010.
Vancouver
1.
Debruyne G, Tenenbaum G. The saddle-point method for general partition functions. INDAGATIONES MATHEMATICAE-NEW SERIES. 2020;31(4):728–38.
IEEE
[1]
G. Debruyne and G. Tenenbaum, “The saddle-point method for general partition functions,” INDAGATIONES MATHEMATICAE-NEW SERIES, vol. 31, no. 4, pp. 728–738, 2020.
@article{8687944,
  abstract     = {{We apply the saddle-point method to derive asymptotic estimates or asymptotic series for the number of partitions of a natural integer into parts chosen from a subset of the positive integers whose associated Dirichlet series satisfies certain analytic properties. This enables grouping in a single statement many cases studied in the literature, as well as a number of new ones. (C) 2020 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.}},
  author       = {{Debruyne, Gregory and Tenenbaum, Gérald}},
  issn         = {{0019-3577}},
  journal      = {{INDAGATIONES MATHEMATICAE-NEW SERIES}},
  keywords     = {{Partitions,Saddle-point method,Asymptotic formula,Abstract partitions}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{728--738}},
  title        = {{The saddle-point method for general partition functions}},
  url          = {{http://doi.org/10.1016/j.indag.2020.06.010}},
  volume       = {{31}},
  year         = {{2020}},
}
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