Periodic binary harmonic functions
| dc.creator | Zaidenberg, Mikhail | |
| dc.date | 2006-08-10 | |
| dc.date.accessioned | 2026-07-07T07:20:37Z | |
| dc.date.available | 2026-07-07T07:20:37Z | |
| dc.description | A function on a (generally infinite) graph $\G$ with values in a field $K$ of characteristic 2 will be called {\it harmonic} if its value at every vertex of $\G$ is the sum of its values over all adjacent vertices. We consider binary pluri-periodic harmonic functions $f: \Z^s\to\F_2=\GF(2)$ on integer lattices, and address the problem of describing the set of possible multi-periods $\bar n=(n_1,...,n_s)\in\N^s$ of such functions. Actually this problem arises in the theory of cellular automata. It occurs to be equivalent to determining, for a certain affine algebraic hypersurface $V_s$ in $\A_{\bar\F_2}^s$, the torsion multi-orders of the points on $V_s$ in the multiplicative group $(\bar\F_2^\times)^s$. In particular $V_2$ is an elliptic cubic curve. In this special case we provide a more thorough treatment. A major part of the paper is devoted to a survey of the subject. | |
| dc.description | 36 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math-ph/0608027 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0608027 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115011 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Number Theory | |
| dc.subject | 11B39, 11T06, 11T99, 31C05, 37B15, 43A99 | |
| dc.title | Periodic binary harmonic functions | |
| dc.type | text |