English

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}
}
R2 v1 2026-06-21T18:48:35.734Z