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Bibliographic Details
Main Authors:	Hasegawa, Takehiro, Komatsu, Takashi, Konno, Norio, Saigo, Hayato, Saito, Seiken, Sato, Iwao, Sugiyama, Shingo
Format:	Preprint
Published:	2020
Subjects:	Combinatorics Number Theory 05C38 (Primary), 05C50, 11F30 (Secondary)
Online Access:	https://arxiv.org/abs/2005.09341
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Table of Contents:

We give a limit theorem with respect to the matrices related to non-backtracking paths of a regular graph. The limit obtained closely resembles the $k$th moments of the arcsine law. Furthermore, we obtain the asymptotics of the averages of the $p^m$th Fourier coefficients of the cusp forms related to the Ramanujan graphs defined by A. Lubotzky, R. Phillips and P. Sarnak.