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Matematicheskie Zametki, 2020, Volume 108, Issue 1, Pages 94–101
DOI: https://doi.org/10.4213/mzm12693 (Mi mzm12693) 		 
This article is cited in 1 scientific paper (total in 1 paper)

New Estimate for Kloosterman Sums with Primes

M. A. Koroleva, M. E. Changab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Moscow State University of Geodesy and Cartography
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DOI: https://doi.org/10.4213/mzm12693
Abstract: We obtain an estimate for a Kloosterman sum with primes for an arbitrary modulus $q$ whose length $X$ satisfies the conditions
$$ q^{1/2+\varepsilon}\le X\ll q^{3/2}. $$
This estimate refines the results obtained earlier by E. Fouvry, I. E. Shparlinski (2011), and the first author (2018, 2019).
Keywords: Kloosterman sums, prime numbers, inverse residues.
Funding agency Grant number
Russian Science Foundation 19-11-00001
The research of the first author was supported by the Russian Science Foundation under grant 19-11-00001.
Received: 12.02.2020
English version:
Mathematical Notes, 2020, Volume 108, Issue 1, Pages 87–93
DOI: https://doi.org/10.1134/S0001434620070081
Bibliographic databases:
Document Type: Article
UDC: 511.33
Language: Russian
Citation: M. A. Korolev, M. E. Changa, “New Estimate for Kloosterman Sums with Primes”, Mat. Zametki, 108:1 (2020), 94–101; Math. Notes, 108:1 (2020), 87–93
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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