Visible points on curve over finite fields

Igor E. Shparlinski, José Felipe Voloch

Research output: Contribution to journalArticlepeer-review


For a prime p and an absolutely irreducible modulo p polynomial f(U, V) E 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.
Original languageEnglish
Pages (from-to)193-199
Number of pages7
JournalBulletin of the Polish Academy of Sciences. Mathematics
Issue number3
Publication statusPublished - 2007


  • points visible from the origin
  • absolutely irreducible polynomial


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