Geodesic
Short exponential sums with a non-integer power of a natural number
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2012), pp. 51-55

Voir la notice de l'article provenant de la source Math-Net.Ru

An estimate for short exponential sums $$S_c(\alpha ;x,y)=\sum_{x-y\le x}e(\alpha [n^c])$$ 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 $\delta=\delta (x,c,A)=\left(2^{[c]+1}-1\right)(A+2,5)\cdot\frac{\ln\ln x}{\ln x}$. 
@article{VMUMM_2012_6_a10,
     author = {P. Z. Rakhmonov},
     title = {Short exponential sums with a non-integer power of a natural number},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {51--55},
     publisher = {mathdoc},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_6_a10/}
}
TY  - JOUR
AU  - P. Z. Rakhmonov
TI  - Short exponential sums with a non-integer power of a natural number
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2012
SP  - 51
EP  - 55
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2012_6_a10/
LA  - ru
ID  - VMUMM_2012_6_a10
ER  - 
%0 Journal Article
%A P. Z. Rakhmonov
%T Short exponential sums with a non-integer power of a natural number
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2012
%P 51-55
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMUMM_2012_6_a10/
%G ru
%F VMUMM_2012_6_a10
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/