Geodesic
Short exponential sums with a non-integer power of a natural number
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2012), pp. 51-55 Cet article a éte moissonné depuis la source Math-Net.Ru

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An estimate for short exponential sums $$S_c(\alpha ;x,y)=\sum_{x-y<n\le x}e(\alpha [n^c])$$ is obtained for $y\ge x^{\frac{1}{2}}\ln^A x$, $x^{1-c}y^{-1}\ln^Ax\le|\alpha|\le 0,5$, $c>2$ and $\|c\|\ge\delta$ where $A$ is a fixed positive number and $\delta=\delta (x,c,A)=\left(2^{[c]+1}-1\right)(A+2,5)\cdot\frac{\ln\ln x}{\ln x}$. 
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     author = {P. Z. Rakhmonov},
     title = {Short exponential sums with a non-integer power of a natural number},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_6_a10/}
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P. Z. Rakhmonov. Short exponential sums with a non-integer power of a natural number. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2012), pp. 51-55. http://geodesic.mathdoc.fr/item/VMUMM_2012_6_a10/

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