Nevanlinna theory via holomorphic forms

نویسندگان

چکیده

This paper re-develops the Nevanlinna theory for meromorphic functions on $\mathbb C$ in viewpoint of holomorphic forms. According to our observation, Nevanlinna's can be formulated by a form. Applying this thought Riemann surfaces, one then extends definition using form $\mathscr S$. With new settings, an analogue \emph{weak S$-exhausted surfaces} is obtained, which viewed as generalization classical and D.$

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Nevanlinna Theory and Holomorphic Mappings between Algebraic Varieties

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 ) . . . . . . . . . ...

متن کامل

Lectures on Nevanlinna theory

Value distribution of a rational function f is controlled by its degree d, which is the number of preimages of a generic point. If we denote by n(a) the number of solutions of the equation f(z) = a, counting multiplicity, in the complex plane C, then n(a) ≤ d for all a ∈ C with equality for all a with one exception, namely a = f(∞). The number of critical points of f in C, counting multiplicity...

متن کامل

Holomorphic Almost Modular Forms

Holomorphic almost modular forms are holomorphic functions of the complex upper half plane which can be approximated arbitrarily well (in a suitable sense) by modular forms of congruence subgroups of large index in SL(2,Z). It is proved that such functions have a rotation-invariant limit distribution when the argument approaches the real axis. An example for a holomorphic almost modular form is...

متن کامل

Nevanlinna Theory and Rational Points

S. Lang [L] conjectured in 1974 that a hyperbolic algebraic variety defined over a number field has only finitely many rational points, and its analogue over function fields. We discuss the Nevanlinna-Cartan theory over function fields of arbitrary dimension and apply it for Diophantine property of hyperbolic projective hypersurfaces (homogeneous Diophantine equations) constructed by Masuda-Nog...

متن کامل

Parametric Nevanlinna-Pick Interpolation Theory

We consider the robust control problem for the system with real uncertainty. This type of problem can be represented with some parameters varying between the boundaries and is formulated as parametric Nevanlinna-Pick interpolation problem in this paper. The existence of a solution for such interpolation problem depends on the positivity of the corresponding Pick matrix with elements belonging t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Pacific Journal of Mathematics

سال: 2022

ISSN: ['1945-5844', '0030-8730']

DOI: https://doi.org/10.2140/pjm.2022.319.55