--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolbox/riemann.m	Wed May 06 14:56:53 2015 +0200
@@ -0,0 +1,23 @@
+function A = riemann(n)
+%RIEMANN    A matrix associated with the Riemann hypothesis.
+%           A = RIEMANN(N) is an N-by-N matrix for which the
+%           Riemann hypothesis is true if and only if
+%           DET(A) = O( N! N^(-1/2+epsilon) ) for every epsilon > 0
+%                                             (`!' denotes factorial).
+%           A = B(2:N+1, 2:N+1), where
+%           B(i,j) = i-1 if i divides j and -1 otherwise.
+%           Properties include, with M = N+1:
+%              Each eigenvalue E(i) satisfies ABS(E(i)) <= M - 1/M.
+%              i <= E(i) <= i+1 with at most M-SQRT(M) exceptions.
+%              All integers in the interval (M/3, M/2] are eigenvalues.
+%
+%           See also REDHEFF.
+
+%           Reference:
+%           F. Roesler, Riemann's hypothesis as an eigenvalue problem,
+%           Linear Algebra and Appl., 81 (1986), pp. 153-198.
+
+n = n+1;
+i = (2:n)'*ones(1,n-1);
+j = i';
+A = i .* (~rem(j,i)) - ones(n-1);