Geodesic
Double character sums with intervals and arbitrary sets
Informatics and Automation, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 258-278

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

We obtain a new bound on certain double sums of multiplicative characters which improves several previous results. This improvement comes from new bounds on the number of collinear triples in finite fields, which is a classical object of study in additive combinatorics.
Keywords: finite field, character sums, collinear triples, multiplicative energy. 
@article{TRSPY_2018_303_a18,
     author = {I. D. Shkredov and I. E. Shparlinski},
     title = {Double character sums with intervals and arbitrary sets},
     journal = {Informatics and Automation},
     pages = {258--278},
     publisher = {mathdoc},
     volume = {303},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2018_303_a18/}
}
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I. D. Shkredov; I. E. Shparlinski. Double character sums with intervals and arbitrary sets. Informatics and Automation, Harmonic analysis, approximation theory, and number theory, Tome 303 (2018), pp. 258-278. http://geodesic.mathdoc.fr/item/TRSPY_2018_303_a18/