On the distribution of rational functions along a curve over \(\mathbb F_p\) and residue races

DOI10.1016/j.jnt.2005.02.002zbMath1068.11043OpenAlexW1976003589MaRDI QIDQ557561

Igor E. Shparlinski, Andrew Granville, Alexandru Zaharescu

Publication date: 30 June 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2005.02.002

zbMATH Keywords

discrepancyaffine curvesdistribution on the torus

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Finite fields and commutative rings (number-theoretic aspects) (11T99) Curves over finite and local fields (11G20) Distribution of integers in special residue classes (11N69)

Related Items (16)

On Sidon sets and asymptotic bases ⋮ Residue races ⋮ On the maximal difference between an element and its inverse in residue rings ⋮ On the difference between an integer and its \(m\)-th power mod \(n\) ⋮ On the concentration of points of polynomial maps and applications ⋮ On the distribution of solutions to polynomial congruences ⋮ Modular hyperbolas ⋮ Distribution of roots of polynomial congruences ⋮ Solution to the index conjecture in zero-sum theory ⋮ Poisson type phenomena for points on hyperelliptic curves modulo \(p\) ⋮ Equidistribution from the Chinese Remainder Theorem ⋮ Average distribution of prime ideals in families of number fields ⋮ Pseudorandom Graphs from Elliptic Curves ⋮ Distribution of the difference of an integer and its \(m\)-th power mod \(n\) over incomplete intervals ⋮ Close values of shifted modular inversions and the decisional modular inversion hidden number problem ⋮ SOLUTIONS TO POLYNOMIAL CONGRUENCES IN WELL-SHAPED SETS

Cites Work

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• The distribution of the values of a rational function modulo a big prime
• Sequences, discrepancies and applications
• Residue races
• Diskrepanz und Distanz von Maßen bezüglich konvexer und Jordanscher Mengen. (Discrepancy and distance of measures with respect to convex and Jordan sets)
• On the distribution of inverses modulo \(n\)
• On the uniform distribution of inverses modulo \(n\)
• Distribution of values of rational maps on the \({\mathbb F}_p\)-points on an affine curve
• The distribution of zeros of an irreducible curve over a finite field
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
• On the distribution of the F_p-points on an affine curve in r dimensions
• The order of inverses mod q
• On Exponential Sums in Finite Fields

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