Geodesic
New estimates for short Kloosterman sums with weights
Izvestiya. Mathematics , Tome 86 (2022) no. 3, pp. 560-585

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In the paper we obtain a new bound for short Kloosterman sums modulo a prime with a weight. The derivation of the bound is based on Karatsuba's method (1993–1995) of estimating incomplete Kloosterman sums and on a modification of the method proposed by Bourgain and Garaev (2014). The theorems proved in the paper refine results obtained earlier by Korolev (2010).
Keywords: short Kloosterman sums, reciprocals modulo a given integer. 
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     author = {N. K. Semenova},
     title = {New estimates for short {Kloosterman} sums with weights},
     journal = {Izvestiya. Mathematics },
     pages = {560--585},
     publisher = {mathdoc},
     volume = {86},
     number = {3},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2022_86_3_a3/}
}
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N. K. Semenova. New estimates for short Kloosterman sums with weights. Izvestiya. Mathematics , Tome 86 (2022) no. 3, pp. 560-585. http://geodesic.mathdoc.fr/item/IM2_2022_86_3_a3/