基於調和多項式的重力透鏡成像數之研究

A Study of the Number of Gravitationally Lensed Images Based on Harmonic Polynomials

楊明訓(Ming-Xun Yang)

指導教授 ： 鄭志豪

國立清華大學/理學院/數學系/碩士(2017年)

摘要

本文探討形式如 $p(z)-overline{z}$ 與 $r(z)-overline{z}$ 兩調和函數的零點個數之上界，其中 $p$ 為多項式、$r$ 為有理函數。該結果有一個令人訝異的應用，是給出了在某個天文模型中重力透鏡成像數的上界。

關鍵字

調和多項式 ； 調和有理函數 ； 重力透鏡

並列摘要

In this thesis, we study bounds for zeros of harmonic functions $p(z)-overline{z}$ and $r(z)-overline{z}$, where $p$ is a polynomial and $r$ is a rational function. A surprising applications of results obtained in this study is that we are able to bound the number of gravitational lensed images in some astronomical models.

並列關鍵字

harmonic polynomial ； harmonic rational function ； gravitational lensing

參考文獻

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