A generalization of the Schur-Siegel-Smyth trace problem

作者：Pratt Kyle^*; Shakan George; Zaharescu Alexandru

来源：Journal of Mathematical Analysis and Applications, 2016, 436(1): 489-500.

DOI：10.1016/j.jmaa.2015.12.003

• Minimal polynomial
• Totally positive algebraic number
• Schur-Siegel-Smyth trace problem

Let a be a totally positive algebraic integer, and define its absolute trace to be Tr(alpha)/deg(alpha), the trace of alpha divided by the degree of alpha. Elementary considerations show that the absolute trace is always at least one, while it is plausible that for any epsilon > 0, the absolute trace is at least 2 - epsilon with only finitely many exceptions. This is known as the Schur-Siegel-Smyth trace problem. Our aim in this paper is to show that the Schur-Siegel-Smyth trace problem can be considered as a special case of a more general problem.

• 出版日期2016-4-1