Geodesic
Estimates for character sums in finite fields of order $p^2$ and $p^3$
Informatics and Automation, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 45-58

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We obtain nontrivial bounds on character sums over “boxes” of volume $p^{n(1/4+\varepsilon)}$ in finite fields of order $p^n$ for $n=2$ and $n=3$. 
@article{TRSPY_2018_303_a4,
     author = {M. R. Gabdullin},
     title = {Estimates for character sums in finite fields of order $p^2$ and $p^3$},
     journal = {Informatics and Automation},
     pages = {45--58},
     publisher = {mathdoc},
     volume = {303},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2018_303_a4/}
}
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M. R. Gabdullin. Estimates for character sums in finite fields of order $p^2$ and $p^3$. Informatics and Automation, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 45-58. http://geodesic.mathdoc.fr/item/TRSPY_2018_303_a4/