Fast Fourier Analysis for SL2over a Finite Field and Related Numerical Experiments

DOI10.1080/10586458.1992.10504252zbMath0773.65091OpenAlexW2029229255MaRDI QIDQ5285858

Daniel N. Rockmore, John D. Lafferty

Publication date: 29 June 1993

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/225374

zbMATH Keywords

Fourier transformfast Fourier transformsfinite fieldrepresentation theoryFourier inversionFourier analysis on finite groupsspectrum of Cayley graphs

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Numerical solutions to equations with linear operators (65J10) Numerical methods for trigonometric approximation and interpolation (65T40) Complexity and performance of numerical algorithms (65Y20) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items

Growth and expansion in algebraic groups over finite fields, The efficient computation of Fourier transforms on semisimple algebras, Survey of Spectra of Laplacians on Finite Symmetric Spaces, Quantum Chaos on Random Cayley Graphs of SL 2[Z/pZ], Expanding graphs and invariant means, Double coset decompositions and computational harmonic analysis on groups, Growth in groups: ideas and perspectives, On the spectral gap for infinite index ``congruence subgroups of \(SL_2(\mathbb{Z})\), On the spectral gap for infinite index ``congruence subgroups of SL\(_2(\mathbb{Z})\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(\lambda_ 1\), isoperimetric inequalities for graphs, and superconcentrators
• Improved upper complexity bounds for the discrete Fourier transform
• Fast Fourier analysis for abelian group extensions
• Discrete groups, expanding graphs and invariant measures. With an appendix by Jonathan D. Rogawski
• Eigenvalues and expanders
• Fast generalized Fourier transforms
• The behaviour of general theta functions under the modular group and the characters of binary modular congruence groups. I, II
• Some Lower and Upper Complexity Bounds for Generalized Fourier Transforms and their Inverses
• Efficient Computation of the Fourier Transform on Finite Groups
• Complex Representations of 𝐺𝐿(2,𝐾) for Finite Fields 𝐾
• Expanders and Diffusers
• Addition requirements for matrix and transposed matrix products
• Fast Fourier Transforms for Metabelian Groups
• Algebraic Graph Theory