On Oka's Extra-Zero Problem
Complex Variables
2011-08-11 v1
Abstract
After the solution of Cousin II problem by K. Oka III in 1939, he thought an {\it extra-zero problem} in 1945 (his posthumous paper) asking if it is possible to solve an arbitrarily given Cousin II problem adding some extra-zeros whose support is disjoint from the given one. By the secondly named author, some special case was affirmatively confirmed in dimension two and a counter-example in dimension three or more was given. The purpose of the present paper is to give a complete solution of this problem with examples and to discuss some new questions.
Cite
@article{arxiv.1108.2076,
title = {On Oka's Extra-Zero Problem},
author = {Makoto Abe and Sachiko Hamano and Junjiro Noguchi},
journal= {arXiv preprint arXiv:1108.2076},
year = {2011}
}