Visible Points on Modular Exponential Curves

• Autorzy: Tsz Ho Chan , Igor E. Shparlinski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11B30: Arithmetic combinatorics; higher degree uniformity
• 11A07: Congruences; primitive roots; residue systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: 58
• Numer: 1
• Strony: 17-22

Daty

wydano

2010

Twórcy

autor

Tsz Ho Chan

• Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, U.S.A.

autor

Igor E. Shparlinski

• Department of Computing, Macquarie University, Sydney, NSW 2109, Australia

Identyfikatory

DOI

10.4064/ba58-1-2