Geodesic
On Double Sums with Multiplicative Characters
Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 174-182.

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

An estimate for double sums of multiplicative characters with additive convolutions of the characteristic functions of sets having small additive doubling is obtained.
Keywords: multiplicative character, additive convolution, sum of sets. 
@article{MZM_2018_104_2_a1,
     author = {A. S. Volostnov},
     title = {On {Double} {Sums} with {Multiplicative} {Characters}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {174--182},
     publisher = {mathdoc},
     volume = {104},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a1/}
}
TY  - JOUR
AU  - A. S. Volostnov
TI  - On Double Sums with Multiplicative Characters
JO  - Matematičeskie zametki
PY  - 2018
SP  - 174
EP  - 182
VL  - 104
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a1/
LA  - ru
ID  - MZM_2018_104_2_a1
ER  - 
%0 Journal Article
%A A. S. Volostnov
%T On Double Sums with Multiplicative Characters
%J Matematičeskie zametki
%D 2018
%P 174-182
%V 104
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a1/
%G ru
%F MZM_2018_104_2_a1
A. S. Volostnov. On Double Sums with Multiplicative Characters. Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 174-182. http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a1/

[1] M.-C. Chang, “On a question of Davenport and Lewis and new character sum bounds in finite fields”, Duke Math. J., 145:3 (2008), 409–442 | DOI | MR | Zbl

[2] H. Davenport, P. Erdős, “The distribution of quadratic and higher residues”, Publ. Math. Debrecen, 2 (1952), 252–265 | MR

[3] A. A. Karatsuba, “Raspredelenie znachenii kharakterov Dirikhle na additivnykh posledovatelnostyakh”, Dokl. AN SSSR, 319:3 (1991), 543–545 | MR | Zbl

[4] A. A. Karatsuba, “Raspredelenie stepennykh vychetov i nevychetov v additivnykh posledovatelnostyakh”, Dokl. AN SSSR, 196 (1971), 759–760 | MR

[5] A. A. Karatsuba, “Arifmeticheskie problemy teorii kharakterov Dirikhle”, UMN, 63:4 (382) (2008), 43–92 | DOI | MR | Zbl

[6] I. D. Shkredov, “Sumsets in quadratic residues”, Acta Arith., 164:3 (2014), 221–243 | DOI | MR | Zbl

[7] A. S. Volostnov, I. D. Shkredov, “Summy multiplikativnykh kharakterov s additivnymi svertkami”, Analiticheskaya i kombinatornaya teoriya chisel, Tr. MIAN, 296, MAIK «Nauka/Interperiodika», M., 2017, 265–279 | DOI | MR | Zbl

[8] J. Friedlander, H. Iwaniec, “Estimates for character sums”, Proc. Amer. Math. Soc., 119:2 (1993), 365–372 | DOI | MR | Zbl

[9] T. Schoen, I. D. Shkredov, “Higher moments of convolutions”, J. Number Theory, 133:1693–1737 (2013) | MR | Zbl

[10] T. Sanders, “The structure theory of sets addition revisited”, Bull. Amer. Math. Soc. (N.S.), 50:1 (2013), 93–127 | DOI | MR | Zbl

[11] S. A. Stepanov, Arifmetika algebraicheskikh krivykh, Nauka, M., 1991 | MR | Zbl

[12] H. Iwaniec, E. Kowalski, Analytic Number Theory, Amer. Math. Soc. Colloq. Publ., 53, Amer. Math. Soc., Providence, RI, 2004 | MR | Zbl

[13] B. Murphy, G. Petridis, O. Roche-Newton, M. Rudnev, I. D. Shkredov, New Results on Sum-Product Type Growth over Fields, arXiv: 1702.01003