报告题目：Salem numbers with minimal trace

主  讲 人：吴强 教授

单      位：西南大学

时      间：2024年6月1日 9:00

地      点：二楼会议室

摘      要：A Salem number \tau of degree 2d is a real algebraic integer greater than 1 whose other conjugates all lie in the closed disc |z| ≤ 1, with at least one on the unit circle. The transformation \alpha=\tau+1/\tau +2 produces a totally positive algebraic integer \alpha of degree d whose all zeros but one are in the interval (0, 4). In this talk, a new method is given to optimize the lower and upper bounds for such totally positive algebraic integer \alpha with given trace and given degree, and then the bounds for s_k. Therefore all Salem numbers of degree 32, 40 and 62 with minimal trace −3, −4 and −6 respectively are found. Consequently, the new lower bounds for degrees of Salem numbers with these minimal traces are given. This is a joint work with Qiong Chen.

简      介：吴强，西南大学数学与统计学院三级教授，博士生导师，重庆数学会常务理事，重庆市学科技术带头人，重庆市高层次引进人才，重庆英才。主要从事计算数论方面的研究，在Math. Computation, J. Number Theory等国际知名杂志发表多篇论文，在代数整数的性质和无理数的有理逼近等方面取得重要成果。多次受邀访问法国、加拿大、香港等国内外科研机构并做学术报告。