Geodesic
Sums of multiplicative characters with additive convolutions
Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 265-279 Cet article a éte moissonné depuis la source Math-Net.Ru

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We obtain new estimates for binary and ternary sums of multiplicative characters with additive convolutions of characteristic functions of sets with small additive doubling. In particular, we improve a result of Mei-Chu Chang. The proof uses the Croot–Sisask almost periodicity lemma. 
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A. S. Volostnov; I. D. Shkredov. Sums of multiplicative characters with additive convolutions. Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 265-279. http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a20/

[1] Aksoy Yazici E., Murphy B., Rudnev M., Shkredov I., Growth estimates in positive characteristic via collisions, E-print, 2015, arXiv: 1512.06613[math.CO]

[2] Chang M.-C., “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

[3] Croot E., Sisask O., “A probabilistic technique for finding almost-periods of convolutions”, Geom. Funct. Anal., 20:6 (2010), 1367–1396 | DOI | MR | Zbl

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

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

[6] Hanson B., Estimates for characters sums with various convolutions, E-print, 2015, arXiv: 1509.04354v1[math.NT]

[7] Iwaniec H., Kowalski E., Analytic number theory, AMS Colloq. Publ., 53, Amer. Math. Soc., Providence, RI, 2004 | MR | Zbl

[8] Karatsuba A. A., “Raspredelenie stepennykh vychetov i nevychetov v additivnykh posledovatelnostyakh”, DAN SSSR, 196:4 (1971), 759–760 | Zbl

[9] Karatsuba A. A., “Summy simvolov Lezhandra ot mnogochlenov vtoroi stepeni s prostymi chislami”, Izv. AN SSSR. Ser. mat., 42:2 (1978), 315–324 | MR | Zbl

[10] Karatsuba A. A., “Raspredelenie znachenii kharakterov Dirikhle na additivnykh posledovatelnostyakh”, DAN SSSR, 319:3 (1991), 543–544 | MR

[11] Karatsuba A. A., “Summy kharakterov s vesami”, Izv. RAN. Ser. mat., 64:2 (2000), 29–42 | DOI | MR | Zbl

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

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

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

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

[16] Tao T., Vu V. H., Additive combinatorics, Cambridge Univ. Press, Cambridge, 2006 | MR | Zbl