Critical points of real entire functions and a conjecture of Pólya |
| |
Authors: | Young-One Kim |
| |
Affiliation: | Department of Mathematics, College of Natural Sciences, Sejong University, Seoul 133--747, Korea |
| |
Abstract: | Let be a nonconstant real entire function of genus and assume that all the zeros of are distributed in some infinite strip , . It is shown that (1) if has nonreal zeros in the region , and has nonreal zeros in the same region, and if the points and are located outside the Jensen disks of , then has exactly critical zeros in the closed interval , (2) if is at most of order , , and minimal type, then for each positive constant there is a positive integer such that for all has only real zeros in the region , and (3) if is of order less than , then has just as many critical points as couples of nonreal zeros. |
| |
Keywords: | P'{o}lya--Wiman conjecture Laguerre--P'{o}lya class Fourier critical point |
|
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 |
|
点击此处可从《Proceedings of the American Mathematical Society》下载全文 |
|