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A NOTE ON SIGNS OF KLOOSTERMAN SUMS
Tekijät: Matomaki K
Kustantaja: FRENCH MATHEMATICAL SOC
Julkaisuvuosi: 2011
Journal: Bulletin De La Societe Mathematique De France
Tietokannassa oleva lehden nimi: BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE
Lehden akronyymi: B SOC MATH FR
Numero sarjassa: 3
Vuosikerta: 139
Numero: 3
Aloitussivu: 287
Lopetussivu: 295
Sivujen määrä: 9
ISSN: 0037-9484
DOI: https://doi.org/10.24033/bsmf.2609
Tiivistelmä
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.
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