On a girth-free variant of the Bourgain-Gamburd machine

DOI10.1016/j.ffa.2023.102225arXiv2111.05751OpenAlexW3211645884MaRDI QIDQ6157013

Ilya D. Shkredov

Publication date: 19 June 2023

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.05751

zbMATH Keywords

continued fractionsquadratic residuesgrowth in groupsmodular hyperbolae

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Linear algebraic groups over finite fields (20G40) Arithmetic combinatorics; higher degree uniformity (11B30)

Cites Work

• Generalization of Selberg's \(\frac {3}{16} \) theorem and affine sieve
• Concentration of points on two and three dimensional modular hyperbolas and applications
• Multilinear exponential sums in prime fields under optimal entropy condition on the sources
• On incidence bounds with Möbius hyperbolae in positive characteristic
• Markov chains on finite fields with deterministic jumps
• A refinement of the Burgess bound for character sums
• Popular products and continued fractions
• Modular hyperbolas and bilinear forms of Kloosterman sums
• Growth and generation in \(\text{SL}_2(\mathbb{Z}/p\mathbb{Z})\).
• Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).
• On additive shifts of multiplicative subgroups
• Growth in SL2 over finite fields
• On Character Sums and Primitive Roots^†
• On the Hidden Shifted Power Problem
• Small Gál sums and applications
• Non-commutative methods in additive combinatorics and number theory
• A Note on the Distribution of Residues and Non-Residues
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