ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS

Bryce Kerr; Ilya D. Shkredov; Igor E. Shparlinski; Alexandru Zaharescu

doi:10.1017/S1474748023000397

ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS

Bryce Kerr, Ilya D. Shkredov, Igor E. Shparlinski, Alexandru Zaharescu

Mathematics

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

Abstract

We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give applications of these results to new bounds on correlations between Salié sums and to a new equidistribution estimate for the set of modular roots of primes.

Original language	English (US)
Journal	Journal of the Institute of Mathematics of Jussieu
DOIs	https://doi.org/10.1017/S1474748023000397
State	Accepted/In press - 2024

Keywords

arithmetic combinatorics
geometry of numbers
Modular roots

ASJC Scopus subject areas

General Mathematics

Online availability

10.1017/S1474748023000397

Cite this

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title = "ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS",

abstract = "We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give applications of these results to new bounds on correlations between Sali{\'e} sums and to a new equidistribution estimate for the set of modular roots of primes.",

keywords = "arithmetic combinatorics, geometry of numbers, Modular roots",

author = "Bryce Kerr and Shkredov, {Ilya D.} and Shparlinski, {Igor E.} and Alexandru Zaharescu",

note = "Publisher Copyright: {\textcopyright} The Author(s), 2024. Published by Cambridge University Press.",

year = "2024",

doi = "10.1017/S1474748023000397",

language = "English (US)",

journal = "Journal of the Institute of Mathematics of Jussieu",

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AU - Shkredov, Ilya D.

AU - Shparlinski, Igor E.

AU - Zaharescu, Alexandru

N1 - Publisher Copyright: © The Author(s), 2024. Published by Cambridge University Press.

PY - 2024

Y1 - 2024

N2 - We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give applications of these results to new bounds on correlations between Salié sums and to a new equidistribution estimate for the set of modular roots of primes.

AB - We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give applications of these results to new bounds on correlations between Salié sums and to a new equidistribution estimate for the set of modular roots of primes.

KW - arithmetic combinatorics

KW - geometry of numbers

KW - Modular roots

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JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

ER -

ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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