1Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A. 2Department of Computing Macquarie University Sydney, NSW 2109, Australia
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 1, pp. 17-22
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.
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
Affiliations des auteurs :
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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author = {Tsz Ho Chan and Igor E. Shparlinski},
title = {Visible {Points} on {Modular} {Exponential} {Curves}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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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
