Periodic harmonic functions on lattices and points count in positive characteristic

Details Periodic harmonic functions on lattices and points count in positive characteristic Periodic harmonic functions on lattices and points count in positive characteristic

2007-06-15

arxiv.org/abs/0706.2228v2

Central European Journal of Mathematics 7, 3 (2009) 365-381

Mathematics

Algebraic Geometry

These are notes on 13p. based on a talk presented during the meeting "Analysis on Graphs and Fractals", the Cardiff University

Scientific paper

10.2478/s11533-009-0029-0

This survey addresses pluri-periodic harmonic functions on lattices with values in a positive characteristic field. We mention, as a motivation, the game "Lights Out" following the work of Sutner, Goldwasser-Klostermeyer-Ware, Barua-Ramakrishnan-Sarkar, Hunzikel-Machiavello-Park e.a.; see also 2 previous author's preprints for a more detailed account. Our approach explores harmonic analysis and algebraic geometry over a positive characteristic field. The Fourier transform allows us to interpret pluri-periods of harmonic functions on lattices as torsion multi-orders of points on the corresponding affine algebraic variety.

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