A NOTE ON SIGNS OF KLOOSTERMAN SUMS



: Matomaki K

Publisher: FRENCH MATHEMATICAL SOC

: 2011

: Bulletin De La Societe Mathematique De France

: BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE

: B SOC MATH FR

: 3

: 139

: 3

: 287

: 295

: 9

: 0037-9484

DOI: https://doi.org/10.24033/bsmf.2609


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.



Last updated on 2024-26-11 at 13:40