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Asymptotics for the sum of powers of distances between power residues modulo a prime

  • M. Z. Garaev
  • S. V. Konyagin
  • Yu. V. Malykhin
Article

Abstract

For fixed q ∈ (0, 4), prime p → ∞, and \(d \leqslant \exp \left( {c\sqrt {\ln p} } \right)\), where c > 0 is a constant, we obtain the asymptotics for the sum of qth powers of distances between neighboring residues of degree d modulo p.

Keywords

STEKLOV Institute Asymptotic Formula Stochasticity Parameter Neighboring Element Quadratic Residue 
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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • M. Z. Garaev
    • 1
  • S. V. Konyagin
    • 2
  • Yu. V. Malykhin
    • 2
  1. 1.Centro de Ciencias MatemáticasUniversidad Nacional Autónoma de MéxicoMorelia, MichoacánMéxico
  2. 2.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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