Reciprocal Polynomials with Small House.pdf

1、西南大學碩士學位論文ReciprocalPolynomialswithSmallHouse姓名：方云飛申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：吳強20080401西南大學碩士學位論文AbstractReciprocalPolynomialwithSmaUHouseM可DFB口sicmo統(tǒng)em口挽∞卻eci口托匆∞仃妒ut口撫D仃死t‘m6盯統(tǒng)eD阿S叩er沈sD口Pn旺W也Qi口唧At‘紈D“Fn凹玩咖i(s20050947)ABST

2、RACTThehouseofanalgebraicintegeristhema硒m以modulusofitsaUconjugate8，denotedby風Wbwritethisthesis，duet0theSchinzelandZ夠∞nha璐’Conjecture：Thereis趾absoluteconstantcl1，叭chthatif同1，then同≥1c1／dwheredisthedegreeof口M瓤lytheoreticall

3、owerboundhadbeenobtainedbydi艉rentpeoplesincethenOneimport鋤tresultisduetoSmythin1971，forthenonreciprocalcaseHeprovedthatif口isanonreciprocalakebraici11teger0fdegreed1，then同≥1log如／d，where％=13247isthereaLlroot0fX3一X一1In1985，

4、Boyd【B085】ga：yeaalgorithmto∞archforthesmauesthou∞0falgebraicintegers0fdegree≤12，andreciprocal2L19ebraichltegersofdegr∞≤16In2007，RhinandⅥ叫Rw】eXtendedhiscomputational跚archtod=29Inthisthesis，weu鼬analgorithmtose甜chforrecipro

5、calalgebr越ciIltegers而thsmauhou∞0fdegr∞≤26【FLMourcomputationuseamethodconcernedthetheor)r0fintegertrans丘nitediameter，au)dlia巧functionandse血linearpr0grammingThesetoolsareusedtogi、，e900dboundsonthecoemcients0ftheminimalpoly

6、nomialofreciprocaLlQInthiswork，wedijscussabothediophantineequationand百veallltheintegersolutionsofX3士8=13y2fFandkeywords：algebr缸cinteger，ma硒maLlmodulus，au)dlia巧function，integertransfinitediameter，semi—in丑nitehnearprogramm