THE TRACE PROBLEM FOR TOTALLY POSITIVE ALGEBRAIC INTEGERS

作     者：Liang, Yanhua Wu, Qiang 

作者机构：SW Univ China Dept Math Chongqing 400715 Peoples R China 

出 版 物：《JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY》 (澳大利亚数学会志)

年 卷 期：2011年第90卷第3期

页      面：341-354页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Natural Science Foundation of Chongqing [2008BB0261] 

主　　题：absolute trace totally positive algebraic integer Salem number explicit auxiliary function semi-infinite linear programming LLL algorithm 

摘      要：Let a be a totally positive algebraic integer of degree d = 2 and alpha(1) = alpha, alpha(2), ... alpha(d), be all its conjugates. We use explicit auxiliary functions to improve the known lower bounds of S-k/d, where S-k = Sigma(d)(i=1) alpha(k)(i) and k = 1, 2, 3. These improvements have consequences for the search of Salem numbers with negative traces.