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Finite Upper Half Planes over Finite Fields

✍ Scribed by Jeff Angel

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 322 KB
Volume: 2
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.1996.0005

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✦ Synopsis

Finite upper half planes have been studied by Terras, Poulos, Celniker, Trimble, and Velasquez. Motivated by Stark's p-adic upper half plane as a p-adic analog of the Poincare ´upper half plane, a finite field of odd characteristic was used as the finite analog of the real line. The analog of the upper half plane was constructed by adjoining the square root of a non-square to the finite field. Since this is not possible with a finite field of even characteristic, this paper will introduce a modification which will enable all finite fields to be considered. After constructing the finite upper half planes, graphs on these planes will be considered. We are interested in the spectrum, girth, diameter, and other combinatorial properties of these graphs.

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