20 06 Recurrence matrices Roland

Determinants Related to Dirichlet Characters Modulo 2, 4 and 8 of binomial Coefficients and the Algebra of Recurrence Matrices

Using recurrence matrices, defined and described with some details, we study a few determinants related to evaluations of binomial coefficients on Dirichlet characters modulo 2, 4 and 8. 1

Recurrence Matrices

Evaluations of Some Determinants of Matrices Related to the Pascal Triangle

We prove several evaluations of determinants of matrices, the entries of which are given by the recurrence ai,j = ai−1,j + ai,j−1, or variations thereof. These evaluations were either conjectured or extend conjectures by Roland Bacher [J. Théorie Nombres Bordeaux 14 (2002), to appear].

ar X iv : h ep - t h / 95 10 06 6 v 1 1 1 O ct 1 99 5 Quartic Anharmonic Oscillator And Random Matrix Theory

In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitean matrices is established. This relationship enables one to present several more or less closed expressions for the oscillator energy. One of such expressions is given in the form of...

1 6 Ju n 20 06 A matrix approach to the computation of quadrature formulas on the unit circle 1 Maŕıa

In this paper we consider a general sequence of orthogonal Laurent polynomials on the unit circle and we first study the equivalences between recurrences for such families and Szegő’s recursion and the structure of the matrix representation for the multiplication operator in Λ when a general sequence of orthogonal Laurent polynomials on the unit circle is considered. Secondly, we analyze the co...