Geodesic
Visible Points on Modular Exponential Curves
Tsz Ho Chan 1   ; Igor E. Shparlinski 2
1 Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A.
2 Department of Computing Macquarie University Sydney, NSW 2109, Australia
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 1, pp. 17-22 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba58-1-2
Keywords: obtain asymptotic formula number visible points gcd which lie box times belong exponential modular curves equiv pmod among other tools recent results additive combinatorics due nbsp bourgain nbsp nbsp garaev play crucial role argument

Tsz Ho Chan  1   ; Igor E. Shparlinski  2

1 Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A.
2 Department of Computing Macquarie University Sydney, NSW 2109, Australia 
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Tsz Ho Chan; Igor E. Shparlinski. Visible Points on Modular Exponential Curves. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 1, pp. 17-22. doi: 10.4064/ba58-1-2

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