2021/03/13 by Junjirō Noguchi, Junjiro Noguchi, Noguchi, Junjiro
Mathematics · #01A60 #32A99 #32E30 #Algebraic and Geometric Analysis #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #History and Overview (math.HO) #Holomorphic and Operator Theory #math.CV #math.HO #msc:01A60 #msc:32A99 #msc:32E30
paper · pdf · doi:10.48550/arxiv.2103.07647
47 pages; A minor revision
openalex publication_date 2021/03/13 · arxiv created 2022/04/28 · arxiv updated 2022/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1943 from September to December Kiyoshi Oka wrote a series of papers numbered from VII to XI, as the research reports to Teiji Takagi (then, Professor of Tokyo Imperial University), in which he solved affirmatively the so-called Levi Problem (Hartogs' Inverse Problem termed by Oka) for unramified Riemann domains over \Cn. This problem which had been left open for more than thirty years then, was the last one of the Three Big Problems summarized by Behnke--Thullen 1934. The papers were hand-written in Japanese, consist of pp.~108 in total, and have not been published by themselves. The aim of the present article is to provide an English translation of the most important, last paper (Part II) with preparation (Part I). At the end of Part I we will discuss a problem which K. Oka left and is still open.