TY - JOUR
T1 - On the distribution of the number of points on a family of curves over finite fields
AU - Mak, Kit Ho
AU - Zaharescu, Alexandru
PY - 2014/7
Y1 - 2014/7
N2 - Let p be a large prime, ℓ ≥ 2 be a positive integer, m ≥ 2 be an integer relatively prime to ℓ and P(x)∈Fp[x] be a polynomial which is not a complete ℓ '-th power for any ℓ ' for which GCD(ℓ ', ℓ) = 1. Let C be the curve defined by the equation yℓ = P(x), and take the points on C to lie in the rectangle [0,p -1]2. In this paper, we study the distribution of the number of points on C inside small rectangles among residue classes modulo m when we move the rectangle around in [0,p -1]2.
AB - Let p be a large prime, ℓ ≥ 2 be a positive integer, m ≥ 2 be an integer relatively prime to ℓ and P(x)∈Fp[x] be a polynomial which is not a complete ℓ '-th power for any ℓ ' for which GCD(ℓ ', ℓ) = 1. Let C be the curve defined by the equation yℓ = P(x), and take the points on C to lie in the rectangle [0,p -1]2. In this paper, we study the distribution of the number of points on C inside small rectangles among residue classes modulo m when we move the rectangle around in [0,p -1]2.
KW - Algebraic curves
KW - Congruences
KW - Rational points
KW - Uniform distribution
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U2 - 10.1016/j.jnt.2014.01.012
DO - 10.1016/j.jnt.2014.01.012
M3 - Article
AN - SCOPUS:84896306255
SN - 0022-314X
VL - 140
SP - 277
EP - 298
JO - Journal of Number Theory
JF - Journal of Number Theory
ER -