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Mat. Zametki, 2010, Volume 88, Issue 4, Pages 529–542 (Mi mz8852)  

This article is cited in 9 scientific papers (total in 9 papers)

Estimates of Character Sums in Finite Fields

S. V. Konyagin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We prove analogs of the Burgess estimates for character sums over $n$-dimensional segments in the field $\mathbb F_{p^n}$.

Keywords: multiplicative character, character sum, Burgess estimate, finite field, polar lattice, Weil estimate, Hölder's inequality

DOI: https://doi.org/10.4213/mzm8852

Full text: PDF file (508 kB)
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English version:
Mathematical Notes, 2010, 88:4, 503–515

Bibliographic databases:

Document Type: Article
UDC: 511.321
Received: 18.08.2009
Revised: 21.10.2009

Citation: S. V. Konyagin, “Estimates of Character Sums in Finite Fields”, Mat. Zametki, 88:4 (2010), 529–542; Math. Notes, 88:4 (2010), 503–515

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. Z. Garaev, “Sums and products of sets and estimates of rational trigonometric sums in fields of prime order”, Russian Math. Surveys, 65:4 (2010), 599–658  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Bourgain J., Garaev M.Z., Konyagin S.V., Shparlinski I.E., “On the hidden shifted power problem”, SIAM J. Comput., 41:6 (2012), 1524–1557  crossref  mathscinet  zmath  isi  elib  scopus
    3. Proc. Steklov Inst. Math., 280 (2013), 61–90  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. Shparlinski I.E., “Products With Variables From Low-Dimensional Affine Spaces and Shifted Power Identity Testing in Finite Fields”, J. Symbolic Comput., 64:SI (2014), 35–41  crossref  mathscinet  zmath  isi  elib  scopus
    5. Hanson B., “Character Sums Over Bohr Sets”, Can. Math. Bul.-Bul. Can. Math., 58:4 (2015), 774–786  crossref  mathscinet  zmath  isi  scopus
    6. M. R. Gabdullin, “On the Squares in the Set of Elements of a Finite Field with Constraints on the Coefficients of Its Basis Expansion”, Math. Notes, 101:2 (2017), 234–249  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Shkredov I.D., Shparlinski I.E., “On Some Multiple Character Sums”, Mathematika, 63:2 (2017), 553–560  crossref  mathscinet  zmath  isi  scopus
    8. Dietmann R. Elsholtz Ch. Shparlinski I.E., “Prescribing the Binary Digits of Squarefree Numbers and Quadratic Residues”, Trans. Am. Math. Soc., 369:12 (2017), 8369–8388  crossref  mathscinet  zmath  isi  scopus
    9. M. R. Gabdullin, “Estimates for character sums in finite fields of order $p^2$ and $p^3$”, Proc. Steklov Inst. Math., 303 (2018), 36–49  mathnet  crossref  crossref  isi  elib
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