Visible Points on Modular Exponential Curves

Volume 58 / 2010

Tsz Ho Chan, Igor E. Shparlinski Bulletin Polish Acad. Sci. Math. 58 (2010), 17-22 MSC: 11A07, 11B30. DOI: 10.4064/ba58-1-2

Abstract

We obtain an asymptotic formula for the number of visible points $(x,y)$, that is, with $\gcd(x,y)=1$, which lie in the box $[1,U] \times [1,V]$ and also belong to the exponential modular curves $y \equiv a g^x \pmod p$. Among other tools, some recent results of additive combinatorics due to J. Bourgain and M. Z. Garaev play a crucial role in our argument.

Authors

  • Tsz Ho ChanDepartment of Mathematical Sciences
    University of Memphis
    Memphis, TN 38152, U.S.A.
    e-mail
  • Igor E. ShparlinskiDepartment of Computing
    Macquarie University
    Sydney, NSW 2109, Australia
    e-mail

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