Algebraic Yuzvinski Formula

作者：Bruno Anna Giordano^*; Virili Simone

来源：Journal of Algebra, 2015, 423: 114-147.

DOI：10.1016/j.jalgebra.2014.10.007

• Algebraic entropy
• Mahler measure
• Yuzvinski Formula
• LCA group
• Endomorphism

Topological entropy is very well-understood for endomorphisms of compact Abelian groups. A fundamental result in this context is the so-called Yuzvinski Formula, which is the key step in finding the topological entropy of any compact group endomorphism. The goal of this paper is to prove a perfect analog of the Yuzvinski Formula for the algebraic entropy, namely, the Algebraic Yuzvinski Formula, giving the value of the algebraic entropy of an endomorphism of a finite-dimensional rational vector space as the Mahler measure of its characteristic polynomial.

• 出版日期2015-2-1