Eigenvalues of Matrices whose Elements are Ramanujan Sums or Kloosterman Sums
Noboru Ushiroya
National Institute of Technology
Wakayama College
Nadacho Gobo Wakayama 644-0023
Japan
Abstract:
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.
Full version: pdf,
dvi,
ps,
latex
(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.
Return to
Journal of Integer Sequences home page
