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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 6, Pages 127–156 (Mi izv4110)  

This article is cited in 1 scientific paper (total in 1 paper)

On the average number of power residues modulo a composite number

M. A. Korolev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We study the behaviour of the quantities $a_{n}(q)$ and $b_{n}(q)$, that is, the number of $n$th power residues in the reduced and complete residue systems modulo a composite number $q$, respectively, where $n\ge2$ is an arbitrary fixed number. In particular, we prove asymptotic formulae for the sum functions $A_{n}(x)$ and $B_{n}(x)$ of these quantities.

Keywords: power residues, average number of power residues, Lehmer–Landau problem.

DOI: https://doi.org/10.4213/im4110

Full text: PDF file (601 kB)
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English version:
Izvestiya: Mathematics, 2010, 74:6, 1225–1254

Bibliographic databases:

UDC: 511
MSC: Primary 11A15; Secondary 11H60
Received: 28.04.2009

Citation: M. A. Korolev, “On the average number of power residues modulo a composite number”, Izv. RAN. Ser. Mat., 74:6 (2010), 127–156; Izv. Math., 74:6 (2010), 1225–1254

Citation in format AMSBIB
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  • https://doi.org/10.4213/im4110
  • http://mi.mathnet.ru/eng/izv/v74/i6/p127

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. F. Adiceam, “Vertical shift and simultaneous Diophantine approximation on polynomial curves”, Proc. Edinb. Math. Soc. (2), 58:1 (2015), 1–26  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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