Mertens equimodular matrices of Redheffer type

Asymptotic behavior of the Mertens function M(n)=∑k=0nμ(k) which is equal to the determinant of the n×n Redheffer matrix, is known to be closely related to the Riemann hypothesis. An infinite matrix whose nth leading principal minor is equal to M(n) for all n≥1 is called a Mertens equimodular matrix. We use Riordan matrices to find a large class of Mertens equimodular matrices, each element of which is called by us a Riordan-Redheffer matrix, briefly an R-R matrix. We also give the generating function for the characteristic polynomials of R-R matrices. As a result, we introduce several examples of R-R matrices that reveal interesting spectral properties. Further, we pose two conjectures on the eigenvalues of those R-R matrices. Finally, we find a sufficient condition for the Riemann hypothesis using the smallest singular value of a R-R matrix.