Visible Points on Modular Exponential Curves
Volume 58 / 2010
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.
