Geodesic
New Estimates of Short Kloosterman Sums
Matematičeskie zametki, Tome 88 (2010) no. 3, pp. 384-398.

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

In this paper, we obtain new, sharper, estimates of short Kloosterman sums.
Keywords: short Kloosterman sum, multiple Kloosterman sum with weights, square-free number, Möbius function. 
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     title = {New {Estimates} of {Short} {Kloosterman} {Sums}},
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     volume = {88},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_3_a6/}
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A. A. Karatsuba. New Estimates of Short Kloosterman Sums. Matematičeskie zametki, Tome 88 (2010) no. 3, pp. 384-398. http://geodesic.mathdoc.fr/item/MZM_2010_88_3_a6/

[1] A. A. Karatsuba, “Raspredelenie obratnykh velichin v koltse vychetov po zadannomu modulyu”, Dokl. RAN., 333:2 (1993), 138–139 | MR | Zbl

[2] A. A. Karatsuba, “Drobnye doli spetsialnogo vida funktsii”, Izv. RAN. Ser. matem., 59:4 (1995), 61–80 | MR | Zbl

[3] A. A. Karatsuba, “Analogi summ Kloostermana”, Izv. RAN. Ser. matem., 59:5 (1995), 93–102 | MR | Zbl

[4] A. A. Karatsuba, “Analogi nepolnykh summ Kloostermana i ikh prilozheniya”, Tatra Mt. Math. Publ., 11 (1997), 89–120 | MR | Zbl

[5] A. A. Karatsuba, “Summy drobnykh dolei spetsialnogo vida funktsii”, Dokl. RAN., 349:3 (1996), 302 | MR | Zbl

[6] A. A. Karatsuba, “Dvoinye summy Kloostermana”, Matem. zametki, 66:5 (1999), 682–687 | MR | Zbl

[7] M. A. Korolëv, “Nepolnye summy Kloostermana i ikh prilozheniya”, Izv. RAN. Ser. matem., 64:6 (2000), 41–64 | MR | Zbl

[8] S. Ramanujan, “Some formulæ in the analytic theory of numbers”, Messenger Math., 45 (1915), 81–84 | Zbl

[9] B. M. Wilson, “Proofs of some formulæ enunciated by Ramanujan”, Proc. London Math. Soc. (2), 21 (1922), 235–255 | DOI | MR | Zbl

[10] L. Carlitz, S. Uchiyama, “Bounds for exponential sums”, Duke Math. J., 24 (1957), 37–41 | DOI | MR | Zbl

[11] M. A. Korolëv, “Korotkie summy Kloostermana s vesami”, Matem. zametki, 88:3 (2010), 415–427 | MR | Zbl