Journal of Integer Sequences, Vol. 21 (2018), Article 18.2.6

Eigenvalues of Matrices whose Elements are Ramanujan Sums or Kloosterman Sums

Noboru Ushiroya
National Institute of Technology
Wakayama College
Nadacho Gobo Wakayama 644-0023


Let cq(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 cq(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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