Fourier analysis and expanding phenomena in finite fields

DOI10.1090/S0002-9939-2012-11338-3zbMath1347.11014arXiv0909.5471OpenAlexW2963249283MaRDI QIDQ4908260

Chun-Yen Shen, Liangpan Li, Derrick N. Hart

Publication date: 5 March 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.5471

zbMATH Keywords

character sumsproductssumsexpanding maps

Mathematics Subject Classification ID

Other character sums and Gauss sums (11T24) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items

Three-term polynomial progressions in subsets of finite fields ⋮ Conditional expanding bounds for two-variable functions over finite valuation rings ⋮ Combinatorial Nullstellensatz approach to polynomial expansion ⋮ The generalized \(k\)-resultant modulus set problem in finite fields ⋮ Expanders on matrices over a finite chain ring, I ⋮ Expanders on Matrices over a Finite Chain Ring, II ⋮ On two-variable expanders over finite rings ⋮ The generalized Erdős-Falconer distance problems in vector spaces over finite fields ⋮ ON THREE-VARIABLE EXPANDERS OVER FINITE FIELDS ⋮ Distinct distances on curves via rigidity ⋮ On three-variable expanders over finite valuation rings ⋮ Algebraic methods in sum-product phenomena ⋮ Moderate expanders over rings ⋮ Conditional expanding bounds for two-variable functions over prime fields ⋮ Four-variable expanders over the prime fields ⋮ Expanding phenomena over matrix rings ⋮ Additive Combinatorics: With a View Towards Computer Science and Cryptography—An Exposition ⋮ Distance sets over arbitrary finite fields ⋮ Products of Differences over Arbitrary Finite Fields ⋮ Expanding phenomena over higher dimensional matrix rings

Cites Work

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• Bounding multiplicative energy by the sumset
• On the sum product estimates and two variables expanders
• Sum-product estimates via directed expanders
• On the size of the set \(A(A + 1)\)
• Sums and products from a finite set of real numbers
• Convexity and sumsets
• Incomplete character sums and polynomial interpolation of the discrete logarithm
• Algebraic methods in sum-product phenomena
• A sum-product estimate in finite fields, and applications
• Combinatorial problems in finite fields and Sidon sets
• An Improved Sum–Product Inequality in Fields of Prime Order
• Slightly improved sum-product estimates in fields of prime order
• A sum-division estimate of reals
• The sum-product estimate for large subsets of prime fields
• An extension of Bourgain and Garaev's sum-product estimates
• On a variant of sum-product estimates and explicit exponential sum bounds in prime fields
• Incidences and the Spectra of Graphs
• On the number of sums and products
• MORE ON THE SUM-PRODUCT PHENOMENON IN PRIME FIELDS AND ITS APPLICATIONS
• An Explicit Sum-Product Estimate in Fp
• Sum-product Estimates in Finite Fields via Kloosterman Sums
• On sums and products of integers
• ON THE NUMBER OF SUMS AND PRODUCTS