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Partitions with multiplicities associated with divisor functions

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Partitions with multiplicities associated with divisor functions. / Berndt, Bruce; Robles, Nicolas; Zaharescu, Alexandru et al.
In: Journal of Mathematical Analysis and Applications, Vol. 533, No. 1, 05.12.2023, p. 127987.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Berndt, B, Robles, N, Zaharescu, A & Zeindler, D 2023, 'Partitions with multiplicities associated with divisor functions', Journal of Mathematical Analysis and Applications, vol. 533, no. 1, pp. 127987. https://doi.org/10.1016/j.jmaa.2023.127987

APA

Berndt, B., Robles, N., Zaharescu, A., & Zeindler, D. (2023). Partitions with multiplicities associated with divisor functions. Journal of Mathematical Analysis and Applications, 533(1), 127987. Advance online publication. https://doi.org/10.1016/j.jmaa.2023.127987

Vancouver

Berndt B, Robles N, Zaharescu A, Zeindler D. Partitions with multiplicities associated with divisor functions. Journal of Mathematical Analysis and Applications. 2023 Dec 5;533(1):127987. Epub 2023 Dec 5. doi: 10.1016/j.jmaa.2023.127987

Author

Berndt, Bruce ; Robles, Nicolas ; Zaharescu, Alexandru et al. / Partitions with multiplicities associated with divisor functions. In: Journal of Mathematical Analysis and Applications. 2023 ; Vol. 533, No. 1. pp. 127987.

Bibtex

@article{5b34fabf5240446aa062c86332691967,
title = "Partitions with multiplicities associated with divisor functions",
abstract = "We consider colored partitions of a positive integer n, where the number of times a particular colored part m may appear in a partition of n is equal to the sum of the powers of the divisors of m. An asymptotic formula is derived for the number of such partitions. We also derive an asymptotic formula for the number of partitions of n into c colors. In order to achieve the desired bounds on the minor arcs arising from the Hardy-Littlewood circle method, we generalize a bound on an exponential sum twisted by a generalized divisor function due to Motohashi.",
author = "Bruce Berndt and Nicolas Robles and Alexandru Zaharescu and Dirk Zeindler",
year = "2023",
month = dec,
day = "5",
doi = "10.1016/j.jmaa.2023.127987",
language = "English",
volume = "533",
pages = "127987",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - Partitions with multiplicities associated with divisor functions

AU - Berndt, Bruce

AU - Robles, Nicolas

AU - Zaharescu, Alexandru

AU - Zeindler, Dirk

PY - 2023/12/5

Y1 - 2023/12/5

N2 - We consider colored partitions of a positive integer n, where the number of times a particular colored part m may appear in a partition of n is equal to the sum of the powers of the divisors of m. An asymptotic formula is derived for the number of such partitions. We also derive an asymptotic formula for the number of partitions of n into c colors. In order to achieve the desired bounds on the minor arcs arising from the Hardy-Littlewood circle method, we generalize a bound on an exponential sum twisted by a generalized divisor function due to Motohashi.

AB - We consider colored partitions of a positive integer n, where the number of times a particular colored part m may appear in a partition of n is equal to the sum of the powers of the divisors of m. An asymptotic formula is derived for the number of such partitions. We also derive an asymptotic formula for the number of partitions of n into c colors. In order to achieve the desired bounds on the minor arcs arising from the Hardy-Littlewood circle method, we generalize a bound on an exponential sum twisted by a generalized divisor function due to Motohashi.

U2 - 10.1016/j.jmaa.2023.127987

DO - 10.1016/j.jmaa.2023.127987

M3 - Journal article

VL - 533

SP - 127987

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -