The orthogonal polynomials with recurrence relation (λn + μn − z)Fn(z) = μn+1 Fn+1(z) + λn−1 Fn−1(z) with two kinds of cubic transition rates λn and μn, corresponding to indeterminate Stieltjes moment problems, are analyzed. We derive generating functions for these two classes of polynomials, which enable us to compute their Nevanlinna matrices. We discuss the asymptotics of the Nevanlinna matr...

0. NOTATIONS AND TERMINOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . 151 (a) D i v i s o r s a n d l ine b u n d l e s . . . . . . . . . . . . . . . . . . . . . . . . . 151 (b) T h e c a n o n i c a l b u n d l e a n d v o l u m e f o r m s . . . . . . . . . . . . . . . . . . . 154 (c) D i f f e r e n t i a l f o r m s a n d c u r r e n t s ( t e r m i n o l o g y ) . . . . . . . . . ...

A complete minimal surface in R is said to be pseudo-algebraic, if its Weierstrass data are defined on a compact Riemann surface finitely many points removed M = M\{P1, . . . , Pn} and extend meromorphically across punctures ([KKM], see also [G]). The punctured Riemann surface M on which the Weierstrass data are defined is called the basic domain. The difference between a complete minimal surfa...

In this note we formulate a conjecture generalizing both the abc conjecture of Masser-Oesterlé and the author’s diophantine conjecture for algebraic points of bounded degree. We also show that the latter conjecture implies the new conjecture. As with most of the author’s conjectures, this new conjecture stems from analogies with Nevanlinna theory. In this particular case the conjecture correspo...

Let 1 ≤ p < ∞ and let μ be a positive finite Borel measure on the unit disk D. The area Nevanlinna-Lebesgue space Np(μ) consists of all measurable functions h on D such that log |h| ∈ Lp(μ), and the area Nevanlinna space N α is the subspace of N p((1 − |z|2)αdν(z)), where α > −1 and ν is area measure on D, consisting of all holomorphic functions. We characterize Carleson measures for N α, defin...

Abstract In this paper, we introduce the notion of an Evertse–Ferretti Nevanlinna constant and compare it with birational introduced by authors in a recent joint paper. We then use to recover several previously known results. This includes 1999 example Faltings from his Baker’s Garden article. also extend theory these constants what call “multidivisor constants,” which allow proximity function ...

The two-dimensional Hamiltonian system (∗) y′(x) = zJH(x)y(x), x ∈ (a,b), where the Hamiltonian H takes non-negative 2× 2-matrices as values, and J := ( 0 −1 1 0 ) , has attracted a lot of interest over the past decades. Special emphasis has been put on operator models and direct and inverse spectral theorems. Weyl theory plays a prominent role in the spectral theory of the equation, relating t...