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Sign changes of Kloosterman sums with almost prime moduli

Xi, Ping

In: Monatshefte für Mathematik, 2015, vol. 177, no. 1, p. 141-163

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    Titre
    • Sign changes of Kloosterman sums with almost prime moduli
    Auteur
    • Xi, Ping. School of Mathematics and Statistics, Xi'an Jiaotong University, 710049, Xi'an, People's Republic of China
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Monatshefte für Mathematik, 2015, vol. 177, no. 1, p. 141-163. Springer Vienna
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:332258
    Summary
    We prove that the Kloosterman sum $$S(1,1;c)$$ S ( 1 , 1 ; c ) changes sign infinitely often as $$c$$ c runs over squarefree moduli with at most 10 prime factors, which improves the previous results of Fouvry and Michel, Sivak-Fischler and Matomäki, replacing 10 by 23, 18 and 15, respectively. The method combines the Selberg sieve, equidistribution of Kloosterman sums and spectral theory of automorphic forms.