Related papers: Recurrence relations of Li coefficients
The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants, that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. We investigate a related set of constants c_n, n =…
A three term recurrence relation is derived for a basis consisting of polynomials multiplied by sines and cosines with large, but fixed frequencies. A numerical method for computing the coefficients of the three term recurrence relation is…
A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…
In this short note, we establish some identities containing sums of binomials with coefficients satisfying third order linear recursive relations. As a result and in particular, we obtain general forms of earlier identities involving…
An analog of the Riemann hypothesis is proved in this paper. Some new integral equations for the functions $\pi(x)$ and $R(x)$ follows. A new effect that is shown is that these function - with essentially different behavior - are the…
We prove an asymptotic formula for the recurrence coefficients of orthogonal polynomials with orthogonality measure $\log \bigl(\frac{2}{1-x}\bigr) {\rm d}x$ on $(-1,1)$. The asymptotic formula confirms a special case of a conjecture by…
We investigate new generalizations of the Meixner polynomials on the lattice $\mathbb{N}$, on the shifted lattice $\mathbb{N}+1-\beta$ and on the bi-lattice $\mathbb{N}\cup (\mathbb{N}+1-\beta)$. We show that the coefficients of the…
Deciding the positivity of a sequence defined by a linear recurrence with polynomial coefficients and initial condition is difficult in general. Even in the case of recurrences with constant coefficients, it is known to be decidable only…
We give the asymptotic behavior of the ratio of two neighboring multiple orthogonal polynomials under the condition that the recurrence coefficients in the nearest neighbor recurrence relations converge.
The multitime multiple recurrences are common in analysis of algorithms, computational biology, information theory, queueing theory, filters theory, statistical physics etc. The theoretical part about them is little or not known. That is…
In this paper we present a simple method for deriving recurrence relations and we apply it to obtain two equations involving the Lerch Phi function and sums of Bernoulli and Euler polynomials. Connections between these results and those…
Is it possible to define a coefficient of correlation which is (a) as simple as the classical coefficients like Pearson's correlation or Spearman's correlation, and yet (b) consistently estimates some simple and interpretable measure of the…
In this paper, we give a connection between the Riemann hypothesis and uniqueness of the Riemann zeta function and an analogue for L-functions.
Considered two linear regression models of a given response variable with some predictor set and its subset. It is shown that there is a linear relationship between coefficients of these models. Some corollaries of the proved theorem is…
We prove a stronger version of Jarden's Theorem for recurrence of powers of recursive functions
We study linear recurrence relations in the character solutions of $Q$-systems obtained from the Kirillov-Reshetikhin modules. We explain how known results on difference $L$-operators lead to a uniform construction of linear recurrences in…
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
We establish a connection between the ratios conjecture for the Riemann zeta-function and a conjecture concerning correlations of convolutions of M\"{o}bius and divisor functions. Specifically, we prove that the ratios conjecture and an…
In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain information about the matrix orthogonal polynomials and functions of second kind associated with a weight matrix. We deduce properties for the…
We consider linear recurrences with polynomial coefficients of Poincar\'e type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a…