【摘要】 本文首先构造了较精确的零级型函数,并用以证明了满足一定条件的零级代数体函数存在Borel方向,结合Valiron和吕以辇的结果即知该条件是代数体函数存在Borel方向的一个充分条件。该条件是精确的,不能再减弱,最后证明了B、4定理对任何超越代数体函数都成立。更多还原

【Abstract】 In this paper I first constructed a more accurate type function of zero order, then Iproved that an algebroid function of zero order satisfying certain condition exists a Boreldirection. With Valiron’s and Lu Yinian’s article, the condition is also sufficient to allalgebroid functions. This is an accurate condition which can’t be weakened. Then I proved thatthe Borel theorem is valid to all transcendental algebroid functions更多还原