Finiteness property and the periodicity of meromorphic functions

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2024-10-17 DOI:10.1007/s10476-024-00042-9

S.-X. Mei, W.-Q. Shen, J. Wang, X. Yao

引用次数: 0

Abstract

In this paper we connect the finiteness property and the periodicity in the study of the generalized Yang’s conjecture and its variations, which involve the inverse question of whether f(z) is still periodic when some differential polynomial in f is periodic. The finiteness property can be dated back to Weierstrass in the characterization of addition law for meromorphic functions. To the best of our knowledge, it seems the first time that the finiteness property is used to investigate generalized Yang’s conjecture, which gives a partial affirmative answer for the meromorphic functions with at least one pole.

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亚纯函数的有限性质与周期性

本文将有限性与周期性联系起来，研究广义杨氏猜想及其变化，这涉及到当f(z)中的某个微分多项式为周期时，f(z)是否仍然是周期的反问题。有限性质可以追溯到weierstrass关于亚纯函数的加法律的描述。据我们所知，这似乎是第一次用有限性质来研究广义杨猜想，它给出了至少有一个极点的亚纯函数的部分肯定答案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.