Visible points on curves over finite fields

• Autorzy: Shparlinski, I. E. , Voloch, J. F.
• Języki publikacji: EN

Abstrakty

EN

For a prime p and an absolutely irreducible modulo p polynomial ƒ(U, V) L 1\U, V] we obtain an asymptotic formula for the number of solutions to the congruence ƒ(x,y) = a (modp) 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.

Słowa kluczowe

EN

points visible from the origin; absolutely irreducible polynomial

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2007
• Tom: Vol. 55, no 3
• Strony: 193-199
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Shparlinski, I. E.

autor

Voloch, J. F.

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

Bibliografia

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• [9] M. Vajaitu and A. Zaharescu, Distribution of values of rational maps on the Fp-points on an affine curve, Monatsh. Math. 136 (2002), 81-86.
• [10] W. G. Zhai, On primitive lattice points in planar domains, Acta Arith. 109 (2003), 1-26.
• [11] Z. Y. Zheng, The distribution of zeros of an irreducible curve over a finite field, J. Number Theory 59 (1996), 106-118.