ON THE SOLVABILITY OF BILINEAR EQUATIONS IN FINITE FIELDS

DOI10.1017/S0017089508004382zbMath1246.11183arXiv0708.2130OpenAlexW2963443196MaRDI QIDQ3529466

Igor E. Shparlinski

Publication date: 13 October 2008

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.2130

Mathematics Subject Classification ID

Other character sums and Gauss sums (11T24) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30) Estimates on character sums (11L40)

Related Items (13)

Asymptotics for the number of directions determined by [n×[n]$[n] \times [n]$ in Fp2${\mathbb F}_p^2$] ⋮ Falconer type functions in three variables ⋮ Expanders on matrices over a finite chain ring, I ⋮ Pinned distance sets, \(k\)-simplices, Wolff's exponent in finite fields and sum-product estimates ⋮ Some remarks on multilinear exponential sums with an application ⋮ Distribution of residues in approximate subgroups of 𝔽_{𝕡}* ⋮ On three-variable expanders over finite valuation rings ⋮ Moderate expanders over rings ⋮ On the solvability of systems of bilinear equations in finite fields ⋮ Expanding phenomena over matrix rings ⋮ Products of Differences over Arbitrary Finite Fields ⋮ Expanding phenomena over higher dimensional matrix rings ⋮ Bounds of trilinear and quadrilinear exponential sums

Cites Work

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• Equations in finite fields with restricted solution sets. I: Character sums
• Equations in finite fields with restricted solution sets. II: Algebraic equations
• A sum-product estimate in finite fields, and applications
• Distribution of matrices with restricted entries over finite fields
• Bilinear character sums over elliptic curves
• Estimates for Character Sums
• A slight improvement to Garaev's sum product estimate
• The sum-product estimate for large subsets of prime fields
• Sum-product Estimates in Finite Fields via Kloosterman Sums
• ESTIMATES FOR THE NUMBER OF SUMS AND PRODUCTS AND FOR EXPONENTIAL SUMS IN FIELDS OF PRIME ORDER

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