Visible Points on Modular Exponential Curves
Tsz Ho Chan ; Igor E. Shparlinski
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010), p. 17-22 / Harvested from The Polish Digital Mathematics Library
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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] × [1,V] and also belong to the exponential modular curves y≡agx(modp). Among other tools, some recent results of additive combinatorics due to J. Bourgain and M. Z. Garaev play a crucial role in our argument.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:286444 
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     volume = {58},
     year = {2010},
     pages = {17-22},
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     language = {en},
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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) pp. 17-22. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba58-1-2/