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Matematicheskie Zametki, 2016, Volume 100, Issue 6, Pages 807–824
DOI: https://doi.org/10.4213/mzm11091 (Mi mzm11091) 		 
This article is cited in 9 scientific papers (total in 9 papers)

On the Squares in the Set of Elements of a Finite Field with Constraints on the Coefficients of Its Basis Expansion

M. R. Gabdullinab

a Lomonosov Moscow State University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Full-text PDF (541 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm11091
Abstract: Recent results of S. Dartyge, C. Mauduit, and A. Sárközy concerning the problem of the number of squares among the elements of a finite field with constraints on the coefficients of its basis expansion are strengthened.
Keywords: missing digits, finite field, squares, character sum.
Funding agency Grant number
Russian Science Foundation 14-11-00702
This work was supported by the Russian Science Foundation under grant 14-11-00702.
Received: 01.06.2016
Revised: 24.07.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 2, Pages 234–249
DOI: https://doi.org/10.1134/S000143461701028X
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: M. R. Gabdullin, “On the Squares in the Set of Elements of a Finite Field with Constraints on the Coefficients of Its Basis Expansion”, Mat. Zametki, 100:6 (2016), 807–824; Math. Notes, 101:2 (2017), 234–249
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm11091
  • https://www.mathnet.ru/eng/mzm/v100/i6/p807
    • This publication is cited in the following 9 articles:
    1. László Mérai, Igor E. Shparlinski, Arne Winterhof, “Character sums over sparse elements of finite fields”, Bulletin of London Math Soc, 56:4 (2024), 1488  crossref
    2. Mehdi Makhul, Arne Winterhof, “Normality of the Thue–Morse function for finite fields along polynomial values”, Res. number theory, 8:3 (2022)  crossref
    3. László Mérai, Arne Winterhof, “Pseudorandom sequences derived from automatic sequences”, Cryptogr. Commun., 14:4 (2022), 783  crossref
    4. L. Reis, “Arithmetic constraints of polynomial maps through discrete logarithms”, J. Number Theory, 229 (2021), 432–443  crossref  mathscinet  isi
    5. C. Dartyge, L. Meral, A. Winterhof, “On the distribution of the rudin-shapiro function for finite fields”, Proc. Amer. Math. Soc., 149:12 (2021), 5013–5023  crossref  mathscinet  isi
    6. C. Swaenepoel, “Trace of products in finite fields”, Finite Fields their Appl., 51 (2018), 93–129  crossref  mathscinet  zmath  isi  scopus
    7. C. Swaenepoel, “Prescribing digits in finite fields”, J. Number Theory, 189 (2018), 97–114  crossref  mathscinet  zmath  isi  scopus
    8. C. Swaenepoel, “On the sum of digits of special sequences in finite fields”, Monatsh. Math., 187:4 (2018), 705–728  crossref  mathscinet  zmath  isi  scopus
    9. R. Dietmann, Ch. Elsholtz, I. E. Shparlinski, “Prescribing the binary digits of squarefree numbers and quadratic residues”, Trans. Am. Math. Soc., 369:12 (2017), 8369–8388  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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