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Mat. Zametki, 2007, Volume 81, Issue 3, Pages 385–404 (Mi mz3681)  

This article is cited in 2 scientific papers (total in 2 papers)

On the Multiplicative Properties Modulo $m$ of Numbers with Missing Digits

N. G. Moshchevitin, I. D. Shkredov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We obtain upper bounds for character sums modulo a composite number over sets of numbers with missing digits in a number system. We derive results on the solvability of congruences of the form $x_1\dotsb x_t\equiv\lambda\pmod{m}$ in the numbers with missing digits and also asymptotic formulas for the number of solutions.

Keywords: number system, number with missing digits, character sum, finite Fourier series

DOI: https://doi.org/10.4213/mzm3681

Full text: PDF file (593 kB)
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English version:
Mathematical Notes, 2007, 81:3, 338–355

Bibliographic databases:

UDC: 511.33
Received: 14.03.2005
Revised: 20.06.2006

Citation: N. G. Moshchevitin, I. D. Shkredov, “On the Multiplicative Properties Modulo $m$ of Numbers with Missing Digits”, Mat. Zametki, 81:3 (2007), 385–404; Math. Notes, 81:3 (2007), 338–355

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. Shparlinski I.E., “Modular hyperbolas”, Jap. J. Math., 7:2 (2012), 235–294  crossref  mathscinet  zmath  isi  elib  scopus
    2. 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
  • Математические заметки Mathematical Notes
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