无零点整函数的原函数有无穷多个零点的情形

Primitive function of no-zero integral function has infinite zeroes

2004年杨重骏提出了如下问题:如果α(z)是非常数整函数,z_0为C中的一点,那么F(z)=∫_(z_0)~ze^(α(w))dw是否一定有无穷多个零点?对上述问题进行了较为深入的研究,给予了否定的回答,并找到超越整函数α(z),当ρ(α)∈R^+/{N^+∪{∞}}时,使F(z)=∫_0~ze^(α(w))dw有无穷多个零点。

In 2004 Yang Dejun put forward the following question: if α( z) is not constant integral function,z_0 is one point of C,then will certainly have infinite zeroes? We have done deep research into the question and given negative answer. The answer is that exceeding the integral function,when ρ( α) ∈ R^+/{ N^+∪ { ∞ } },F( z) = ∫_0~ze^(α(w)) dwwill have infinite zeroes.