M. A. Korolev, “Short Kloosterman Sums with Weights”, Mat. Zametki, 88:3 (2010), 415–427; Math. Notes, 88:3 (2010), 374

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Matematicheskie Zametki, 2010, Volume 88, Issue 3, Pages 415–427
DOI: https://doi.org/10.4213/mzm8814 (Mi mzm8814)

This article is cited in 16 scientific papers (total in 16 papers)

Short Kloosterman Sums with Weights

M. A. Korolev

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (482 kB) Citations (16)

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DOI: https://doi.org/10.4213/mzm8814

Abstract: We obtain a new estimate for Kloosterman sums with weights in which the number of summands is significantly less than any arbitrarily small fixed power of the modulus.

Keywords: Kloosterman sum with weight, prime number, Euler function, Möbius function, square-free number.

Received: 20.08.2009

English version:
Mathematical Notes, 2010, Volume 88, Issue 3, Pages 374–385
DOI: https://doi.org/10.1134/S0001434610090105

Bibliographic databases:

Document Type: Article

UDC: 511.33

Language: Russian

Citation: M. A. Korolev, “Short Kloosterman Sums with Weights”, Mat. Zametki, 88:3 (2010), 415–427; Math. Notes, 88:3 (2010), 374–385

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm8814

https://doi.org/10.4213/mzm8814

https://www.mathnet.ru/eng/mzm/v88/i3/p415

This publication is cited in the following 16 articles:

N. K. Semenova, “On estimating an inhomogeneous Kloosterman sum by the Karatsuba method”, Math. Notes, 116:3 (2024), 527–540
Moubariz Z. Garaev, Igor E. Shparlinski, “On the distribution of modular inverses from short intervals”, Mathematika, 69:4 (2023), 1183
M. A. Korolev, “Vinogradov's sieve and an estimate for an incomplete Kloosterman sum”, Sb. Math., 213:2 (2022), 216–234
N. K. Semenova, “New estimates for short Kloosterman sums with weights”, Izv. Math., 86:3 (2022), 560–585
M. A. Korolev, “Short Kloosterman Sums with Primes”, Math. Notes, 106:1 (2019), 89–97
M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661
M. A. Korolev, “Elementary Proof of an Estimate for Kloosterman Sums with Primes”, Math. Notes, 103:5 (2018), 761–768
M. A. Korolev, “Divisors of a quadratic form with primes”, Proc. Steklov Inst. Math., 303 (2018), 154–170
M. A. Korolev, “The estimate of weighted Kloosterman sums by additive shift”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 221–229
M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43
M. A. Korolev, “Karatsuba's method for estimating Kloosterman sums”, Sb. Math., 207:8 (2016), 1142–1158
M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Math. Notes, 100:6 (2016), 820–827
M. A. Korolev, “Methods of estimating of incomplete Kloosterman sums”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 230–245
J. Bourgain, M. Z. Garaev, “Sumsets of reciprocals in prime fields and multilinear Kloosterman sums”, Izv. Math., 78:4 (2014), 656–707
Bourgain J. Garaev M.Z., “Kloosterman Sums in Residue Rings”, Acta Arith., 164:1 (2014), 43–64
A. A. Karatsuba, “New Estimates of Short Kloosterman Sums”, Math. Notes, 88:3 (2010), 347–359

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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