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n iS 1. Let fCzD = V a z , where z = re and is any n=0 sequence of complex numbers, be a non-constant entire function. We set MCrD = max |fCzD|, fKrD = max < |ajr n > |z|=r n20 and vCrD » max < n:/Xr3 = |an|r n >. Then MCrD, and vCr) are called respectively the maximum modulus, the maximum term and the rank of the maximum term of fCz) for |z|sr. It is well known that log MCr3 and log /jCr3 are indefinitely increasing convex function of log r and vCr5 is a nondecreasing integer valued functiondoi:10.1515/dema-1988-0102 fatcat:rpigaxgl3fefpiupe4ovbjmv4m