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Strange and pseudo-differentiable functions with applications to prime partitions

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

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Strange and pseudo-differentiable functions with applications to prime partitions. / Dong, Anji; Robles, Nicolas; Zaharescu, Alexandru et al.
In: Research in Number Theory, Vol. 11, No. 2, 52, 30.06.2025.

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

Harvard

Dong, A, Robles, N, Zaharescu, A & Zeindler, D 2025, 'Strange and pseudo-differentiable functions with applications to prime partitions', Research in Number Theory, vol. 11, no. 2, 52. https://doi.org/10.1007/s40993-025-00628-8

APA

Dong, A., Robles, N., Zaharescu, A., & Zeindler, D. (2025). Strange and pseudo-differentiable functions with applications to prime partitions. Research in Number Theory, 11(2), Article 52. https://doi.org/10.1007/s40993-025-00628-8

Vancouver

Dong A, Robles N, Zaharescu A, Zeindler D. Strange and pseudo-differentiable functions with applications to prime partitions. Research in Number Theory. 2025 Jun 30;11(2):52. Epub 2025 Apr 26. doi: 10.1007/s40993-025-00628-8

Author

Dong, Anji ; Robles, Nicolas ; Zaharescu, Alexandru et al. / Strange and pseudo-differentiable functions with applications to prime partitions. In: Research in Number Theory. 2025 ; Vol. 11, No. 2.

Bibtex

@article{d8eff9d873ac42718fd9013c3a71280e,
title = "Strange and pseudo-differentiable functions with applications to prime partitions",
abstract = "Let pPr(n) denote the number of partitions of n into r-full primes. We use the Hardy–Littlewood circle method to find the asymptotic of pPr(n) as n→∞. This extends previous results in the literature of partitions into primes. We also show an analogue result involving convolutions of von Mangoldt functions and the zeros of the Riemann zeta-function. To handle the resulting non-principal major arcs we introduce the definition of strange functions and pseudo-differentiability.",
keywords = "Secondary: 11L07, 11L20, 11M26, Strange functions, Von Mangoldt function, Weights associated to partitions, Pseudo-differentiable functions, Inclusion–exclusion, Hardy–Littlewood circle method, Zeros of the zeta function, Primary: 11P55, 11P82, 26A24, Exponential sums",
author = "Anji Dong and Nicolas Robles and Alexandru Zaharescu and Dirk Zeindler",
year = "2025",
month = jun,
day = "30",
doi = "10.1007/s40993-025-00628-8",
language = "English",
volume = "11",
journal = "Research in Number Theory",
issn = "2522-0160",
publisher = "Springer International Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - Strange and pseudo-differentiable functions with applications to prime partitions

AU - Dong, Anji

AU - Robles, Nicolas

AU - Zaharescu, Alexandru

AU - Zeindler, Dirk

PY - 2025/6/30

Y1 - 2025/6/30

N2 - Let pPr(n) denote the number of partitions of n into r-full primes. We use the Hardy–Littlewood circle method to find the asymptotic of pPr(n) as n→∞. This extends previous results in the literature of partitions into primes. We also show an analogue result involving convolutions of von Mangoldt functions and the zeros of the Riemann zeta-function. To handle the resulting non-principal major arcs we introduce the definition of strange functions and pseudo-differentiability.

AB - Let pPr(n) denote the number of partitions of n into r-full primes. We use the Hardy–Littlewood circle method to find the asymptotic of pPr(n) as n→∞. This extends previous results in the literature of partitions into primes. We also show an analogue result involving convolutions of von Mangoldt functions and the zeros of the Riemann zeta-function. To handle the resulting non-principal major arcs we introduce the definition of strange functions and pseudo-differentiability.

KW - Secondary: 11L07, 11L20, 11M26

KW - Strange functions

KW - Von Mangoldt function

KW - Weights associated to partitions

KW - Pseudo-differentiable functions

KW - Inclusion–exclusion

KW - Hardy–Littlewood circle method

KW - Zeros of the zeta function

KW - Primary: 11P55, 11P82, 26A24

KW - Exponential sums

U2 - 10.1007/s40993-025-00628-8

DO - 10.1007/s40993-025-00628-8

M3 - Journal article

VL - 11

JO - Research in Number Theory

JF - Research in Number Theory

SN - 2522-0160

IS - 2

M1 - 52

ER -