A1 Refereed original research article in a scientific journal
On the Balog–Ruzsa theorem in short intervals
Authors: Sun Yu-Chen
Publisher: OXFORD UNIV PRESS
Publication year: 2023
Journal: Quarterly Journal of Mathematics
Journal name in source: QUARTERLY JOURNAL OF MATHEMATICS
Journal acronym: Q J MATH
Number of pages: 22
ISSN: 0033-5606
eISSN: 1464-3847
DOI: https://doi.org/10.1093/qmath/haad017
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://doi.org/10.1093/qmath/haad017
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/179736099
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
In this paper we give a short interval version of the Balog-Ruzsa theorem concerning bounds for the L-1 norm of the exponential sum over r-free numbers. In particular, when r= 2, for H >= N9/17+epsilon, we have the lower bound resultintegral(T)vertical bar Sigma vertical bar(n-N vertical bar> H-1/3,and for H >= N18+29+(epsilon), we have the upper bound resultintegral(T)vertical bar Sigma vertical bar(n-N vertical bar> H-1/6 when H >= N9/17+epsilon.
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