A1 Refereed original research article in a scientific journal
A NOTE ON SIGNS OF KLOOSTERMAN SUMS
Authors: Matomaki K
Publisher: FRENCH MATHEMATICAL SOC
Publication year: 2011
Journal: Bulletin De La Societe Mathematique De France
Journal name in source: BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE
Journal acronym: B SOC MATH FR
Number in series: 3
Volume: 139
Issue: 3
First page : 287
Last page: 295
Number of pages: 9
ISSN: 0037-9484
DOI: https://doi.org/10.24033/bsmf.2609
Abstract
We prove that the sign of Kloosterman sums Kl(1, 1; n) changes infinitely often as n runs through the square-free numbers with at most 15 prime factors. This improves on a previous result by Sivak-Fischler who obtained 18 instead of 15. Our improvement comes from introducing an elementary inequality which gives lower and upper bounds for the dot product of two sequences whose individual distributions are known.
We prove that the sign of Kloosterman sums Kl(1, 1; n) changes infinitely often as n runs through the square-free numbers with at most 15 prime factors. This improves on a previous result by Sivak-Fischler who obtained 18 instead of 15. Our improvement comes from introducing an elementary inequality which gives lower and upper bounds for the dot product of two sequences whose individual distributions are known.
UTU Research Portal