In this paper, we investigate the properties of Ramanujan polynomials, a family of reciprocal polynomials with real coefficients originating from Ramanujan’s work. We begin by finding their number of real zeros, establishing a bound on their sizes, and determining their limiting values. Next, we prove that all nonreal zeros of Ramanujan polynomials lie on the unit circle, and are asymptotically...

We study the simultaneous zeros of a random family of d polynomials in d variables over the p-adic numbers. For a family of natural models, we obtain an explicit constant for the expected number of zeros that lie in the d-fold Cartesian product of the p-adic integers. Considering models in which the maximum degree that each variable appears is N , this expected value is pdblogp Nc ( 1 + p−1 + p...

This paper studies the Schrödinger operator with Morse potential Vk(u) = 1 4e 2u + keu on a right half-line [u0,∞), and determines the Weyl asymptotics of eigenvalues for constant boundary conditions at the endpoint u0. In consequence it obtains information on the location of zeros of the Whittaker function Wκ,μ(x), for fixed real parameters κ, x with x > 0, viewed as an entire function in the ...

the main idea of this paper is to study the dependence between the probability of default and the recovery rate on credit portfolio and to seek empirically this relationship. we examine the dependence between pd and rr by theoretical approach. for the empirically methodology, we use the bootstrapped quantile regression and the simultaneous quantile regression. these methods allow to determinate...