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# Finite analogues of non-Euclidean spaces and Ramanujan graphs

@article{Bannai2004FiniteAO, title={Finite analogues of non-Euclidean spaces and Ramanujan graphs}, author={Eiichi Bannai and Osamu Shimabukuro and Hajime Tanaka}, journal={Eur. J. Comb.}, year={2004}, volume={25}, pages={243-259} }

- Published 2004 in Eur. J. Comb.
DOI:10.1016/S0195-6698(03)00110-0

This is a compa nion paper of “Finite Euclidean graphs and Ramanujan graphs” by the same authors. Finite analogues of the Poincar ́ e upper half plane, i.e., finite upper half plane graphs, were studied by many researchers, including Terras, Evans etc. Finally, it was proved by combining works of A. Weil, P. Deligne, R. Evans, H. Stark, N. Katz, W. Li and many others, that the finite upper half plane graphs of valency q + 1 over the finite field Fq are all Ramanujan graphs. In this paper, we… CONTINUE READING

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