Calculation of the indicator of an entire function of rational order in terms of its taylor coefficients

Abstract

By using both the Pólya theorem on the connection between the growth of an entire exponential function and the location of singularities of its Borel transform and the analog of this result for finite-order entire functions (due to Mclntyre), we obtain estimates for the indicator of the growth of an entire function in terms of its Taylor coefficients and, in some cases, determine this indicator exactly.