For a known random Dirichlet series of infinite order on the whole plane, the authors construct a Dirirchlet series such that the growth of both series referring to the type function is the same. Thus one can study the growth of the former by studying the coefficient and exponent of the latter.
运用覆盖曲面的几何方法,证明了代数体函数族一个正规定理:设F为区域D内的一族k值代数体函数,且F的分支点是孤立的.若对pD,总存在一个含于D内的邻域U(p),使得在U(p)内,对每个ftF存在3个判别的复数at1,at2,at3,满足sum from i=1 to 3 (U(p),ati,ft)≤1,则F在D内正规.
