柯倫布猜想在多項式上的數值研究

Abstract

本論文介紹柯倫布猜想（Korenblum conjecture）在多項式上的數值結果。柯倫布常數（Korenblum's constant ）在多項式上可以更容易地利用不同的解根和數值積分方法找出。最後，我們考慮柯倫布猜想在某些分式函數上，能找出目前最佳的柯倫布常數的上界。

In this study we give a brief description of numerical results on Korenblum's conjecture for polynomials. The Korenblum's constant will be found out numerically by using different numerical integration methods and some methods for solving roots. It can be solved easily a little bit for Korenblum's conjecture under polynomials. Finally, we consider Korenblum's conjecture for some kinds of fractional functions and obtain a better upper bound of Korenblum's constant.