时间：2025年9月26日（周五）14:00-15:00
地点：E4-233
主持人： 理论科学研究院 Paolo Dolce
主讲人：David Masser
讲座主题：Lower bounds for heights over function fields
讲座摘要: After introducing the Lehmer Question (unanswered since 1933), we discuss lower bounds of Lehmer type for Neron-Tate heights on elliptic curves over the function field C(t) (before last year there were apparently no such estimates in the published literature). Then Silverman proved a result using the "Fourier Method". I will describe an alternative method through auxiliary polynomials and an approach first used by Sieburg in his 1983 thesis (since then hardly developed in the published literature). That method is based on an analogue of Mahler's p-adic transcendence techniques which could be crudely described as t-adic. At about the same time Looper and Silverman proved a partial analogue for abelian surfaces, and our method applies there too.
