Central European Journal of Mathematics

, Volume 7, Issue 3, pp 365–381 | Cite as

Periodic harmonic functions on lattices and points count in positive characteristic

Review Article

Abstract

This survey deals with pluri-periodic harmonic functions on lattices with values in a field of positive characteristic. We mention, as a motivation, the game “Lights Out” following the work of Sutner [20], Goldwasser- Klostermeyer-Ware [5], Barua-Ramakrishnan-Sarkar [2, 19], Hunzikel-Machiavello-Park [12] e.a.; see also [22, 23] for a more detailed account. Our approach uses harmonic analysis and algebraic geometry over a field of positive characteristic.

Keywords

Cellular automaton Chebyshev-Dickson polynomial Convolution operator Lattice Finite field Discrete Fourier transform Discrete harmonic function Pluri-periodic function 

MSC

11B39 11T06 11T99 31C05 37B15 43A99 

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Copyright information

© © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Institut FourierUniversité Grenoble IGrenobleFrance

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