The Rolf Nevanlinna Prize is awarded once every four years at the International Congress of Mathematicians by the International Mathematical Union for outstanding contributions in mathematical aspects of information sciences. The 2010 recipient was Daniel Spielman, who was cited for “smoothed analysis of Linear Programming, algorithms for graph-based codes, and applications of graph theory to N...

Abstract. A crucial ingredient in the recent discovery by Ablowitz, Halburd, Herbst and Korhonen [2], [15] that a connection exists between discrete Painlevé equations and (finite order) Nevanlinna theory is an estimate of the integrated average of log |f(z + 1)/f(z)| on |z| = r. We obtained essentially the same estimate in our previous paper [8] independent of Halburd et al [14]. We continue o...

If f is a meromorphic function in the complex plane, R. Nevanlinna noted that its characteristic function T r, f could be used to categorize f according to its rate of growth as |z| r → ∞. Later H. Milloux showed for a transcendental meromorphic function in the plane that for each positive integer k, m r, f k /f o T r, f as r → ∞, possibly outside a set of finite measure where m denotes the pro...

In this paper, by meromorphic functions we will always mean meromorphic functions in the complex plane C. We adopt the standard notations of the Nevanlinna theory of meromorphic functions as explained in [6]. It will be convenient to let E denote any set of positive real numbers of finite linear measure, not necessarily the same at each occurrence. For a non-constant meromorphic function h, we ...

Simulations of finite temperature quantum systems provide imaginary frequency Green's functions that correspond one-to-one to experimentally measurable real-frequency spectral functions. However, due the bad conditioning continuation transform from real frequencies, established methods tend either wash out features at high frequencies or produce with unphysical negative parts. Here, we show exp...

We describe the real quasi-exactly solvable locus of the PT-symmetric quartic using Nevanlinna parametrization. MSC: 81Q05, 34M60, 34A05

First, an abstract scheme of constructing biorthogonal rational systems related to some interpolation problems is proposed. We also present a modification of the famous step-by-step process of solving the NevanlinnaPick problems for Nevanlinna functions. The process in question gives rise to three-term recurrence relations with coefficients depending on the spectral parameter. These relations c...