We examine the electrostatic properties of exceptional and regular zeros of Xm-Laguerre and Xm-Jacobi polynomials. Since there is a close connection between the electrostatic properties of the zeros and the stability of interpolation on the system of zeros, we can deduce an Egerváry-Turán type result as well. The limit of the energy on the regular zeros is also investigated.

Abstract: Necessary and sufficient conditions for the reachability and observability of the positive electrical circuits composed of resistors, coils, condensators and voltage sources are established. Definitions of the input-decoupling zeros, output-decoupling zeros and input-output decoupling zeros of the positive electrical circuits are proposed. Some properties of the decoupling zeros of po...

Monotonicity of zeros of orthogonal Laurent polynomials associated with a strong distribution with respect to a parameter is discussed. A natural analog of a classical result of A. Markov is proved. Recent results of Ismail and Muldoon based on the Hellman-Feynman theorem are also extended to a monotonicity criterion for zeros of Laurent polynomials. Results concerning the behaviour of extreme ...

We study convexity properties of the zeros of some special functions that follow from the convexity theorem of Sturm. We prove results on the intervals of convexity for the zeros of Laguerre, Jacobi and ultraspherical polynomials, as well as functions related to them, using transformations under which the zeros remain unchanged. We give upper as well as lower bounds for the distance between con...

This note is concerned with the zeros of holomorphic Hecke cusp forms of large weight on the modular surface. The zeros of such forms are symmetric about three geodesic segments and we call those zeros that lie on these segments, real. Our main results give estimates for the number of real zeros as the weight goes to infinity. Mathematics Subject Classification (2010). Primary: 11F11, 11F30. Se...

There is a well-known opposition, about the ethics of belief, between the "Victorian" position heralded by Clifford's famous maxim:"It is wrong, always, everywhere, and for everyone, to believe anything on insufficient evidence", and the so-called "pragmatist" view put forward by William James in his essay "The Will to Believe", according to which believing may be under the control of the will,...

1. Teichmuller was the first to bring out the important role played by quadratic differentials in extremal problems in the theory of functions. He indicated [3] the behavior in the small of certain important curves associated with them. It remained for Schaeffer and Spencer [2, Chap. Ill] to carry out this study in full detail. While they speak explicitly only of hyperelliptic differentials, th...

Article history: Received 17 May 2009 Available online 19 January 2011 Communicated by Gilles Schaeffer