複素平面上の有理型函数及び代数型函数の値分布

复平面上有理函数和代数函数的值分布

• 批准号: 06640219
• 负责人: 藤解 和也
• 金额: $ 0.9万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06640219/
• 关键词: 有理型函数; Nevanlinna理論; Hayman予想; 零点分布; 値共有問題; 代数型函数; 代数型面; Picard定数

本研究の当初の目的の一つが、いわゆるHaymanの予想の解決であった。即ち、複素平面上の有理型函数fとその二階導函数f″が零点を持たないとき、対数的導函数f′/fの逆数は高々一次多項式に帰着される(このとき、f(z)=f_<exc>(z):=exp(Az+B)または(Az+B)^<-n>,A,B∈C,n∈N)ことの証明である。30年間以上も未解決であったこの予想は、しかしながら本研究を開始して間もなく、J.K.Langley氏により完全に解決された。それ故、導函数の零点が有する特異性を別な方向から論ずるべく、Haymanの予想とも密接に関連する次の問題の考察が研究目的となった:有理型函数fの零点分布とその各k階導函数f^<(k)>(n【greater than or equal】k【greater than or equal】1)の零点分布が不変と仮定したn=3、或はn=2かつfの零点の収束指数有限条件のもとで、得られたこの問題の解はf=f_<exc>である。これにより、f_<exc>を除けばどの函数も高階導函数の零点分布が特異ではないことを、本研究で確かめたと考える。第二の研究目的は、n価代数型面のPicard定数に関するOzawa‐Sawadaの定理の拡張であった。Picard定数の最大値2nそして2n-1をもつn価代数型面S(n=3,4)をそれぞれ特徴付けるため、Ozawa‐Sawadaはその面の位数が有限、即ちSを定義するn価整代数型函数yの位数が有限であることを仮定した。本研究では、複素平面上の有理型函数に関して得た結果を応用して、n=3のときにSawada‐Tohgeが、n=4の場合にNiino‐Tohgeがそれぞれ別の手法を用いて、位数有限性の仮定を取り除くことに成功した。特にNiino‐Tohgeが用いた手法は、一般のn(【greater than or equal】3)に対しても適用可能であり、今後の研究に寄与する処は少

The purpose of this study is to solve the problem of Hayman at the beginning. That is to say, the rational function of rational type on the complex plane, the leading function of the rational function f, the zero point of the rational function f, the leading function of the number, the inverse function of the number, the inverse function, the inverse function, the polynomial function, the linear function, the rational function, the leading function, the inverse function, the inverse function, the linear function, the rational function, the rational function, the second leading function, the rational function, the second leading function, the rational function, the second leading function, the leading function, the inverse function, the leading function, the rational function, the second leading function, the rational function, the second leading function, the rational function, the leading function, the inverse function, the inverse function, the linear function, the rational function, the leading function, the inverse function, the inverse function, the linear function, the rational function, the rational function, the leading function, the inverse function, the inverse function In the past 30 years or more, we have not been able to solve the problem in the past 30 years. At the beginning of this study, we have completed the study with the help of J.K. Langley's study. Therefore, the zero point of the leading function has some characteristics, the direction is different, the direction is different, and the Hayman expects that the second order of the problem is closely linked. The purpose of the study is: rational function f, zero distribution, every k leading function f ^ & lt; (k) & gt (n [greater than or equal] k [greater than or equal] 1) the distribution of zero points does not determine the number of points 3, or the number of zero points of the bundle index is limited, so that the solution of the problem of zero point distribution can be solved. In addition to the fact that the distribution of zeros is special, this study is intended to make sure that there is a lot of research in this study. The second "purpose of the study", n "algebraic profile", "Picard number", "Ozawa-Sawada" theorem, "algebra", "number", "fixed number", "Ozawa-Sawada" theorem. Picard defines the number of digits of the algebraic profile S (num 3pj4), the number of digits of the Ozawa-Sawada surface is limited, that is, the number of digits of the integer algebraic function y is defined by the number of digits of the integer algebraic function y. In this study, we obtained the results of rational function analysis on the complex element plane. The results showed that we used the methods of "Sawada-Tohge", "3", "Sawada-Tohge", "4", "Niino-Tohge", and "number of digits are limited." Special Niino-Tohge uses "gimmick", "general" ([greater than or equal] 3) "may be used", and future "research" will be sent to you less.

项目成果

Kiyoshi Niino: "Some functional equations and Picard constants of algebroid surfaces" Journal of the Mathematical Society of Japan. 48(発表予定). (1996)

Kiyoshi Niino：“代数曲面的一些函数方程和皮卡德常数”，日本数学会杂志 48（待出版）。

Yoshihide Okumura: "Grobal real analytic length parameters and angle parameters for Teichmuller spaces and the geometry of hyperbolic transformations" 京都大学数理解析研究所講究録(Complex Analysis on Hyperbolic 3‐Manifolds). 882. 77-88 (1994)

Yoshihide Okumura：“Teichmuller 空间的全局实解析长度参数和角度参数以及双曲变换的几何”《双曲 3 流形复分析》，京都大学，882. 77-88 (1994)。

Kazunari Sawada: "A remark on three‐sheeted algebroid surfaces whose Picard constants are five" Kodai Mathematical Journal. (発表予定).

Kazunari Sawada：“关于皮卡德常数为 5 的三片代数曲面的评论”Kodai Mathematical Journal（即将出版）。

Kazuya Tohge: "Meromorphic functions which share the value zero with their first two derivatives" Complex Variables Theory and Application. (発表予定).

Kazuya Tohge：“与前两个导数共享零值的亚纯函数”复变量理论与应用（即将介绍）。

Yoshihide Okumura: "Grobal real analytic length parameters for Teichmuller spaces" Hiroshima Mathematical Journal. 26(発表予定). (1996)

Yoshihide Okumura：“Teichmuller 空间的全局实解析长度参数”广岛数学杂志 26（待出版）。