M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Mat. Zametki, 100:6 (2016), 838–846; Math. Notes, 100:6 (2016), 820

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Matematicheskie Zametki, 2016, Volume 100, Issue 6, Pages 838–846
DOI: https://doi.org/10.4213/mzm11048 (Mi mzm11048)

This article is cited in 11 scientific papers (total in 11 papers)

On Short Kloosterman Sums Modulo a Prime

M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences

Full-text PDF (440 kB) Citations (11)

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DOI: https://doi.org/10.4213/mzm11048

Abstract: Using the Karatsuba method, we obtain new estimates for Kloosterman sums modulo a prime, which, under certain constraints on the number of summands, are sharper than similar estimates found earlier.

Keywords: Kloosterman sum, Karatsuba method, inverse quantities.

Funding agency	Grant number
Russian Science Foundation	14-50-00005
This work was supported by the Russian Science Foundation under grant 14-50-00005.

Received: 22.12.2015
Revised: 27.08.2016

English version:
Mathematical Notes, 2016, Volume 100, Issue 6, Pages 820–827
DOI: https://doi.org/10.1134/S0001434616110213

Bibliographic databases:

Document Type: Article

UDC: 517

Language: Russian

Citation: M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Mat. Zametki, 100:6 (2016), 838–846; Math. Notes, 100:6 (2016), 820–827

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Linking options:

https://www.mathnet.ru/eng/mzm11048

https://doi.org/10.4213/mzm11048

https://www.mathnet.ru/eng/mzm/v100/i6/p838

Related presentations:

On the zeros of Epstein zeta-function, Kloosterman sums and some other problems of number theory
M. A. Korolev, November 19, 2018 14:00

This publication is cited in the following 11 articles:

N. K. Semenova, “On estimating an inhomogeneous Kloosterman sum by the Karatsuba method”, Math. Notes, 116:3 (2024), 527–540
M. A. Korolev, “Vinogradov's sieve and an estimate for an incomplete Kloosterman sum”, Sb. Math., 213:2 (2022), 216–234
M. A. Korolev, “Kloosterman sums over primes of composite moduli”, Res. Number Theory, 6:2 (2020), 24
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, “New estimate for a Kloosterman sum with primes for a composite modulus”, Sb. Math., 209:5 (2018), 652–659
M. A. Korolev, “Divisors of a quadratic form with primes”, Proc. Steklov Inst. Math., 303 (2018), 154–170
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, “On a Diophantine inequality with reciprocals”, Proc. Steklov Inst. Math., 299 (2017), 132–142
M. A. Korolev, “Methods of estimating of incomplete Kloosterman sums”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 230–245

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

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Abstract page:	577
Full-text PDF :	82
References:	56
First page:	19

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