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The Distribution of Zeros of an Irreducible Curve over a Finite Field

✍ Scribed by Zhiyong Zheng

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 473 KB
Volume: 59
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0090

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✦ Synopsis

Let f (x, y) be a polynomial defined over Z in two variables of total degree d 2, and let Vp=[(x, y) # C p : f(x, y)#0 (mod p)] for each prime p, where C p = [(x, y) # Z 2 : 0 x<p and 0 y<p]. In this paper, we show that if f (x, y) is absolutely irreducible modulo p for all sufficiently large p, then we have the following distribution formula for the zeros of f (x, y) modulo p, :

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