On congruences with products of variables from short intervals and applications

DOI10.1134/S0081543813010057zbMath1301.11041arXiv1203.0017OpenAlexW1972147519MaRDI QIDQ2446173

Igor E. Shparlinski, Moubariz Z. Garaev, Sergei V. Konyagin, Jean Bourgain

Publication date: 16 April 2014

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.0017

zbMATH Keywords

congruences in many variablesestimates on character sumsshort intervalsresidue systems

Mathematics Subject Classification ID

Other character sums and Gauss sums (11T24) Congruences in many variables (11D79) Congruences; primitive roots; residue systems (11A07) Estimates on character sums (11L40)

Related Items (21)

The congruence $ax_1x_2\cdots x_k + bx_{k+1}x_{k+2}\cdots x_{2k} \equiv c \pmod p$ ⋮ On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s ⋮ Points on polynomial curves in small boxes modulo an integer ⋮ Concentration of points on curves in finite fields ⋮ Correcting noisy exponentiation black-boxes modulo a prime ⋮ Modular hyperbolas ⋮ Double exponential sums with exponential functions ⋮ On distribution of elements of subgroups in arithmetic progressions modulo a prime ⋮ Double character sums with intervals and arbitrary sets ⋮ Congruences involving product of intervals and sets with small multiplicative doubling modulo a prime and applications ⋮ ON SOME MULTIPLE CHARACTER SUMS ⋮ Products with variables from low-dimensional affine spaces and shifted power identity testing in finite fields ⋮ Bilinear forms in Weyl sums for modular square roots and applications ⋮ On sums of Kloosterman and Gauss sums ⋮ Discrete spheres and arithmetic progressions in product sets ⋮ Product of subsets of small intervals and points on exponential curves modulo a prime ⋮ VISIBLE POINTS ON EXPONENTIAL CURVES ⋮ Multiplicative congruences with variables from short intervals ⋮ Distribution of exponential functions modulo a prime power ⋮ Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition ⋮ Bounds of trilinear and quadrilinear exponential sums

Cites Work

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• On multiplicative congruences
• Estimates of character sums in finite fields
• Concentration of points on two and three dimensional modular hyperbolas and applications
• The equation \(x_1x_2=x_3x_4+\lambda \) in fields of prime order and applications
• On a generalisation of a Lehmer problem
• Successive-minima-type inequalities
• Factorization in generalized arithmetic progressions and application to the Erdős-Szemerédi sum-product problems
• The congruence \(x_ 1x_ 2\equiv x_ 3x_ 4\pmod p\), the equation \(x_ 1x_ 2=x_ 3x_ 4\), and mean values of character sums
• The congruence \(x_1 x_2 \equiv x_3 x_4\) and mean values of character sums
• On the distribution of points on multidimensional modular hyperbolas.
• POWER-FREE VALUES OF THE POLYNOMIAL t₁⋯t_r−1
• Estimates for Character Sums
• Arithmetic problems in the theory of Dirichlet characters
• High order moments of character sums
• Weighted character sums
• On the Hidden Shifted Power Problem
• On the concentration of points on modular hyperbolas and exponential curves
• MORE ON THE SUM-PRODUCT PHENOMENON IN PRIME FIELDS AND ITS APPLICATIONS
• The divisor problem for arithmetic progressions

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