Sign changes of Kloosterman sums with almost prime moduli

Ping Xi

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arXiv · 1310.8623

Sign changes of Kloosterman sums with almost prime moduli

Ping Xi

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Abstract

We prove that the Kloosterman sum $S(1,1;c)$ can change sign infinitely often as $c$ runs over squarefree moduli with at most 10 prime factors, which improves the previous results of E. Fouvry and Ph. Michel, J. Sivak-Fischler and K. 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.

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Ping Xi. 2014-06-04. Sign changes of Kloosterman sums with almost prime moduli. https://arxiv.org/abs/1310.8623

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