Geodesic
On Kloosterman Sums with Oscillating Coefficients
Canadian mathematical bulletin, Tome 42 (1999) no. 3, pp. 285-290

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DOI

In this paper we prove: for any positive integers $a$ and $q$ with $\left( a,\,q \right)\,=\,1$ , we have uniformly $$\sum\limits_{\begin{matrix} n\le N\\ (n,q)=1,n\bar{n}\equiv 1(\,\bmod \,q)\\\end{matrix}}{\mu (n)e(\frac{a\bar{n}}{q})\ll Nd(q)\left\{ \frac{{{\log }^{\frac{5}{2}}}N}{{{q}^{\frac{1}{2}}}}+\frac{{{q}^{\frac{1}{5}}}{{\log }^{\frac{13}{5}}}N}{{{N}^{\frac{1}{5}}}} \right\}.}$$ This improves the previous bound obtained by D. Hajela, A. Pollington and B. Smith [5].
DOI : 10.4153/CMB-1999-034-8
Mots-clés : 10G10, Kloosterman sums, oscillating coefficients, estimate 
Deng, Peiming. On Kloosterman Sums with Oscillating Coefficients. Canadian mathematical bulletin, Tome 42 (1999) no. 3, pp. 285-290. doi: 10.4153/CMB-1999-034-8
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     author = {Deng, Peiming},
     title = {On {Kloosterman} {Sums} with {Oscillating} {Coefficients}},
     journal = {Canadian mathematical bulletin},
     pages = {285--290},
     year = {1999},
     volume = {42},
     number = {3},
     doi = {10.4153/CMB-1999-034-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-034-8/}
}
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