Visible Points on Curves over Finite Fields

• Autorzy: Igor E. Shparlinski , José Felipe Voloch
• Języki publikacji: EN

Abstrakty

EN

For a prime p and an absolutely irreducible modulo p polynomial f(U,V) ∈ ℤ[U,V] we obtain an asymptotic formula for the number of solutions to the congruence f(x,y) ≡ a (mod p) in positive integers x ≤ X, y ≤ Y, with the additional condition gcd(x,y) = 1. Such solutions have a natural interpretation as solutions which are visible from the origin. These formulas are derived on average over a for a fixed prime p, and also on average over p for a fixed integer a.

Kategorie tematyczne

• 11L40: Estimates on character sums
• 11K38: Irregularities of distribution, discrepancy
• 11A07: Congruences; primitive roots; residue systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: 55
• Numer: 3
• Strony: 193-199

Daty

wydano

2007

Twórcy

autor

Igor E. Shparlinski

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

autor

José Felipe Voloch

• Department of Mathematics, University of Texas, Austin, TX 78712, U.S.A.

Identyfikatory

DOI

10.4064/ba55-3-1