Abstract
Let be the -Paley graph defined on the finite field . It is notoriously difficult to improve the trivial upper bound on the clique number of . In this paper, we investigate the connection between Gauss sums over a finite field and the maximum cliques of their corresponding generalized Paley graphs. We show that the trivial upper bound on the clique number of is tight if and only if , which strengthens the previous related results by Broere-Döman-Ridley and Schneider-Silva. We also obtain a new simple proof of Stickelberger's theorem on evaluating semi-primitive Gauss sums.
Citation
Chi Hoi Yip. "Gauss sums and the maximum cliques in generalized Paley graphs of square order." Funct. Approx. Comment. Math. 66 (1) 119 - 138, March 2022. https://doi.org/10.7169/facm/1981
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