
Sign changes of Kloosterman sums with almost prime moduli
Ping XI.
Monatshefte für Mathematik:
2014
,23
Abstract
We prove that the Kloosterman sum $S(1,1;c)$ changes sign infinitely often as $c$ runs over squarefree moduli with at most 10 prime factors, which improves the previous results of Fouvry and Michel, SivakFischler 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.

Quadratic residues and nonresidues for infinitely many PiatetskiShapiro primes
Ping Xi.
Acta Mathematica Sinica, English Series:
2013
,Volume 29, Issue 3
,515522
Abstract
In this paper, we prove a quantitative version of the statement that every nonempty finite subset of ℕ+ is a set of quadratic residues for infinitely many primes of the form [n c ] with 1 ≤ c ≤ 243/205. Correspondingly, we can obtain a similar result for the case of quadratic nonresidues under reasonable assumptions. These results generalize the previous ones obtained by Wright in certain aspects.

A note on the moments of Kloosterman sums
Ping Xi, Yuan Yi.
Proceedings of the American Mathematical Society:
2013
,141
,12331240
Abstract
In this note, we deduce an asymptotic formula for even power moments of Kloosterman sums based on the important work of N. M. Katz on Kloosterman sheaves. In a similar manner, we can also obtain an upper bound for odd power moments. Moreover, we shall give an asymptotic formula for odd power moments of absolute Kloosterman sums. Consequently, we find that there are infinitely many $ a＼bmod p$ such that $ S(a,1;p)＼gtrless 0$ as $ p＼rightarrow +＼infty .$

Generalized D. H. Lehmer problem over short intervals
Ping Xi, Yuan Yi.
Glasgow Mathematical Journal:
2011
,Volume 53
,293299

On character sums over flat numbers
Ping Xi, Yuan Yi.
Journal of Number Theory:
2010
,Volume 130, Issue 5
,1234–1240
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