Exponential sums over Möbius convolutions with applications to partitions

Debmalya Basak; Nicolas Robles; Alexandru Zaharescu

doi:10.4153/S0008414X24000701

Exponential sums over Möbius convolutions with applications to partitions

Debmalya Basak, Nicolas Robles, Alexandru Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We establish bounds for exponential sums twisted by generalized Möbius functions and their convolutions. As an application, we prove asymptotic formulas for certain weighted chromatic partitions by using the Hardy-Littlewood circle method. Lastly, we provide an explicit formula relating the contributions from the major arcs with a sum over the zeros of the Riemann zeta-function.

Original language	English (US)
Journal	Canadian Journal of Mathematics
Early online date	Jan 9 2025
DOIs	https://doi.org/10.4153/S0008414X24000701
State	E-pub ahead of print - Jan 9 2025

Keywords

Exponential sums
Hardy-Littlewood circle method
Möbius convolutions
Riemann zeta-function
weighted partitions

ASJC Scopus subject areas

General Mathematics

Online availability

10.4153/S0008414X24000701

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AU - Robles, Nicolas

AU - Zaharescu, Alexandru

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PY - 2025/1/9

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N2 - We establish bounds for exponential sums twisted by generalized Möbius functions and their convolutions. As an application, we prove asymptotic formulas for certain weighted chromatic partitions by using the Hardy-Littlewood circle method. Lastly, we provide an explicit formula relating the contributions from the major arcs with a sum over the zeros of the Riemann zeta-function.

AB - We establish bounds for exponential sums twisted by generalized Möbius functions and their convolutions. As an application, we prove asymptotic formulas for certain weighted chromatic partitions by using the Hardy-Littlewood circle method. Lastly, we provide an explicit formula relating the contributions from the major arcs with a sum over the zeros of the Riemann zeta-function.

KW - Exponential sums

KW - Hardy-Littlewood circle method

KW - Möbius convolutions

KW - Riemann zeta-function

KW - weighted partitions

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JF - Canadian Journal of Mathematics

ER -

Exponential sums over Möbius convolutions with applications to partitions

Abstract

Keywords

ASJC Scopus subject areas

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