## Memoirs of the College of Science, University of Kyoto. Series A: Mathematics

### Notes on meromorphic covariants

Yukio Kusunoki

#### Abstract

The present paper is based essentially upon $R$. Nevanlinna's theory [I] on Abelian integrals. In § 1 we shall establish the first fundamental theorem of R. Nevanlinna (Theorem 2) for the meromorphic covariants of order $n (n=0, \pm 1, \pm 2, \ldots )$ (cf. sec. 4) on an arbitrary open Riemann surface and give some of its applications in § 2, where Theorem 3 corresponds to Shimizu-Ahlfors’ theorem for covariants.

#### Article information

Source
Mem. College Sci. Univ. Kyoto Ser. A Math., Volume 30, Number 3 (1957), 243-249.

Dates
First available in Project Euclid: 20 August 2009

https://projecteuclid.org/euclid.kjm/1250777009

Digital Object Identifier
doi:10.1215/kjm/1250777009

Mathematical Reviews number (MathSciNet)
MR94449

Zentralblatt MATH identifier
0091.25306

#### Citation

Kusunoki, Yukio. Notes on meromorphic covariants. Mem. College Sci. Univ. Kyoto Ser. A Math. 30 (1957), no. 3, 243--249. doi:10.1215/kjm/1250777009. https://projecteuclid.org/euclid.kjm/1250777009