On Oka's Extra-Zero Problem

Details On Oka's Extra-Zero Problem On Oka's Extra-Zero Problem

2011-08-10

arxiv.org/abs/1108.2076v1

Mathematics

Complex Variables

Scientific paper

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.

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