Visible Points on Modular Exponential Curves

Tsz Ho Chan, and Igor E. Shparlinski. "Visible Points on Modular Exponential Curves." Bulletin of the Polish Academy of Sciences. Mathematics 58.1 (2010): 17-22. <http://eudml.org/doc/286444>.

@article{TszHoChan2010,
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] × [1,V] and also belong to the exponential modular curves $y ≡ ag^\{x\} (mod p)$. Among other tools, some recent results of additive combinatorics due to J. Bourgain and M. Z. Garaev play a crucial role in our argument.},
author = {Tsz Ho Chan, Igor E. Shparlinski},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {primitive roots; counting integers with special properties},
language = {eng},
number = {1},
pages = {17-22},
title = {Visible Points on Modular Exponential Curves},
url = {http://eudml.org/doc/286444},
volume = {58},
year = {2010},
}

TY - JOUR
AU - Tsz Ho Chan
AU - Igor E. Shparlinski
TI - Visible Points on Modular Exponential Curves
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2010
VL - 58
IS - 1
SP - 17
EP - 22
AB - 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] × [1,V] and also belong to the exponential modular curves $y ≡ ag^{x} (mod p)$. Among other tools, some recent results of additive combinatorics due to J. Bourgain and M. Z. Garaev play a crucial role in our argument.
LA - eng
KW - primitive roots; counting integers with special properties
UR - http://eudml.org/doc/286444
ER -