Expansion in \(\mathrm{SL}_d(\mathcal O_K/I)\), \(I\) square-free.

DOI10.4171/JEMS/302zbMath1269.20044arXiv1001.3664OpenAlexW1811931273MaRDI QIDQ653296

Péter Pál Varjú

Publication date: 9 January 2012

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.3664

zbMATH Keywords

Cayley graphsexpandersrandom walks on groupssymmetric generating setsaffine sievesalgebraic groups over number fieldsproperty tau

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Other combinatorial number theory (11B75) Linear algebraic groups over global fields and their integers (20G30) Arithmetic combinatorics; higher degree uniformity (11B30)

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Cites Work

• \(\lambda_ 1\), isoperimetric inequalities for graphs, and superconcentrators
• Expansion and random walks in \(\text{SL}_d(\mathbb{Z}/p^n\mathbb{Z})\). II.
• Expansion and random walks in \(\text{SL}_d(\mathbb{Z}/p^n\mathbb{Z})\). I.
• Eigenvalues and expanders
• Semigroups containing proximal linear maps
• Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).
• Effective Bezout identities in \({\mathbb{Q}}[z_ 1,\dots ,z_ n\)]

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