On the concentration of points of polynomial maps and applications

DOI10.1007/s00209-011-0959-7zbMath1285.11027OpenAlexW2091439828MaRDI QIDQ1925734

Igor E. Shparlinski, Alina Ostafe, Javier Cilleruelo, Moubariz Z. Garaev

Publication date: 19 December 2012

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-011-0959-7

zbMATH Keywords

orbitsadditive combinatoricspolynomial congruencesVinogradov's mean value theoremvisible points

Mathematics Subject Classification ID

Related Items (25)

SOLUTIONS TO DIAGONAL CONGRUENCES WITH VARIABLES RESTRICTED TO A BOX ⋮ Points on polynomial curves in small boxes modulo an integer ⋮ Concentration of points on curves in finite fields ⋮ On the distribution of solutions to polynomial congruences ⋮ Correcting noisy exponentiation black-boxes modulo a prime ⋮ Additive energy and a large sieve inequality for sparse sequences ⋮ Modular hyperbolas ⋮ Double character sums with intervals and arbitrary sets ⋮ Points on curves in small boxes and applications ⋮ Lehmer points and visible points on affine varieties over finite fields ⋮ The finite Littlewood problem in \(\mathbb{F}_p\) ⋮ Subgroups generated by rational functions in finite fields ⋮ Polynomial iteration in characteristic \(p\) ⋮ Groups generated by iterations of polynomials over finite fields ⋮ Unlikely intersections over finite fields: polynomial orbits in small subgroups ⋮ Identity testing and interpolation from high powers of polynomials of large degree over finite fields ⋮ ON BILINEAR EXPONENTIAL AND CHARACTER SUMS WITH RECIPROCALS OF POLYNOMIALS ⋮ Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition ⋮ Polynomial values in affine subspaces of finite fields ⋮ Interpolation and Approximation of Polynomials in Finite Fields over a Short Interval from Noisy Values ⋮ A large sieve inequality for power moduli ⋮ Expansions of quadratic maps in prime fields ⋮ Close values of shifted modular inversions and the decisional modular inversion hidden number problem ⋮ SOLUTIONS TO POLYNOMIAL CONGRUENCES IN WELL-SHAPED SETS ⋮ Large sieve estimate for multivariate polynomial moduli and applications

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• EXPANSION OF ORBITS OF SOME DYNAMICAL SYSTEMS OVER FINITE FIELDS
• On the concentration of points on modular hyperbolas and exponential curves
• MORE ON THE SUM-PRODUCT PHENOMENON IN PRIME FIELDS AND ITS APPLICATIONS
• Visible Points on Curves over Finite Fields
• On polynomial congruences

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