値分布論をモデルとした複素函数論の超離散的関数論への変換と諸分野への応用

Material type: 文書・図像類

Author: 藤解, 和也ほか

Publisher: 金沢大学理工研究域電子情報通信学系

Publication date: 2019-06-20

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Note (General)：: 超離散一次分数変換を差分作用素とした有界開区間上のトロピカル値分布論の確立などLaine, Korhonen, Heittokangas, Y-Y. Zhengと複素関数方程式についての知見を得、Gundersen, Steinmetzと共同して有理型函数の5対複素数共有に関する未解決問題を肯定的に...

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https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16K05194/

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Material Type: 文書・図像類
Title: 値分布論をモデルとした複素函数論の超離散的関数論への変換と諸分野への応用
Author/Editor: 藤解, 和也
Toge, Kazuya
Author Heading: 藤解, 和也
Toge, Kazuya
Publication, Distribution, etc.: 金沢大学理工研究域電子情報通信学系
Publication Date: 2019-06-20
Publication Date (W3CDTF): 2019-06-20
Alternative Title: The adaptation of complex function theory to ultradiscrete function theory modeled on value distribution theories and its application to various fields
Periodical title: 平成30(2018)年度科学研究費補助金基盤研究(C) 研究成果報告書 = 2018 Fiscal Year Final Research Report
No. or year of volume/issue: 2016-04-01 - 2019-03-31
Volume: 2016-04-01 - 2019-03-31
Pages: 6p.-
Text Language Code: jpn
Subject Heading: トロピカル・ネバンリンナ理論
超離散方程式
複素差分方程式
複素線型微分方程式
超越有理型函数
Mason's theorem
exponential polynomial
国際研究者交流
Target Audience: 一般
Note (General): 超離散一次分数変換を差分作用素とした有界開区間上のトロピカル値分布論の確立などLaine, Korhonen, Heittokangas, Y-Y. Zhengと複素関数方程式についての知見を得、Gundersen, Steinmetzと共同して有理型函数の5対複素数共有に関する未解決問題を肯定的に解決した。石崎, Wen, Li, J-H. Zhengも加わり指数函数多項式の零点分布、差分版radicalによるMason's theoremの類似、有理型函数の差分商評価の精密化で最良の評価を導いた。更にLinと値の共有概念の差分化に関しても最良の結果を得るなど当初目的に叶う研究成果を上げた。
Laine and I have set up the tropical value distribution theory on a finite open interval by means of an ultradiscrete linear fractional transformation as shift, while some results from function theory have been tropicalized together with Liu. Collaborating with Laine, Korhonen, Heittokangas and Y-Y. Zhang, we have made a progress on complex functional equations, while it was the joint work with Gundersen and Steinmetz to have settled an open problem on the uniqueness of two meromorphic functions sharing five pairs of values affirmatively. Furthermore, we invited Ishizaki, Wen, Li and JーH. Zheng and studied the zero distribution of exponential polynomials, an analogue of Mason's theorem with differential radical and a refinement of the estimate of difference ratio of meromorphic functions each of which provides the best possible result in a certain sense. Finally, Lin and I studied the difference counterpart of sharing values jointly and obtained a sharp result concerning this concept.
研究課題/領域番号:16K05194, 研究期間(年度):2016-04-01 - 2019-03-31
出典：「値分布論をモデルとした複素函数論の超離散的関数論への変換と諸分野への応用」研究成果報告書　課題番号16K05194（KAKEN：科学研究費助成事業データベース（国立情報学研究所））（https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-16K05194/16K05194seika/）を加工して作成
DOI: 10.24517/00053760
Access Restrictions: 限定公開
Related Material: https://kaken.nii.ac.jp/search/?qm=30260558
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16K05194/
https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-16K05194/16K05194seika/
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 金沢大学 : 金沢大学学術情報リポジトリKURA