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Eigenvalues of Matrices whose Elements are Ramanujan Sums or Kloosterman Sums
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Noboru Ushiroya

National Institute of Technology

Wakayama College

Nadacho Gobo Wakayama 644-0023

Japan

**Abstract:**

Let *c*_{q}(*n*) be the Ramanujan sum and let
*S*(*m*, *n*;*q*) be the Kloosterman sum. We study
the eigenvalues of *q* × *q* matrices whose (*m*,
*n*) entry is *c*_{q}(*m* - *n*) or
*S*(*m*, *n*; *q*), where *q* is a fixed
positive integer. We also study the eigenvalues of matrices whose
entries are sums of Ramanujan sums or sums of Kloosterman sums.

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(Concerned with sequences
A054532
A054533
A054534
A054535.)

Received August 23 2017; revised versions received November 28 2017; February 14 2018.
Published in *Journal of Integer Sequences*, March 6 2018.

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