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An analogue of the Weierstrass ζ-function in characteristic p

100%

Voloch J.

Acta Arithmetica

1997

tom 79

nr 1

1-6

Visible Points on Curves over Finite Fields

63%

Shparlinski I., Voloch J.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

tom 55

nr 3

193-199

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.

A local-global criterion for dynamics on ℙ¹

63%

Silverman J., Voloch J.

Acta Arithmetica

2009

tom 137

nr 3

285-294

Ograniczanie wyników

2 Acta Arithmetica

1 Bulletin of the Polish Academy of Sciences. Mathematics

3 Voloch J.

1 Shparlinski I.

1 Silverman J.

1 2009

1 2007

1 1997

Wyniki wyszukiwania

An analogue of the Weierstrass ζ-function in characteristic p

Visible Points on Curves over Finite Fields

A local-global criterion for dynamics on ℙ¹