Lehmer's Problem, McKay's Correspondence, and $2,3,7$

Details Lehmer's Problem, McKay's Correspondence, and $2,3,7$ Lehmer's Problem, McKay's Correspondence, and $2,3,7$

2002-04-02

arxiv.org/abs/math/0204040v1

Mathematics

Geometric Topology

Scientific paper

This paper addresses a long standing open problem due to Lehmer in which the triple 2,3,7 plays a notable role. Lehmer's problem asks whether there is a gap between 1 and the next smallest algebraic integer with respect to Mahler measure. The question has been studied in a wide range of contexts including number theory, ergodic theory, hyperbolic geometry, and knot theory; and relates to basic questions such as describing the distribution of heights of algebraic integers, and of lengths of geodesics on arithmetic surfaces. This paper focuses on the role of Coxeter systems in Lehmer's problem. The analysis also leads to a topological version of McKay's correspondence.

Affiliated with

Also associated with

No associations

Rating

Lehmer's Problem, McKay's Correspondence, and $2,3,7$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Lehmer's Problem, McKay's Correspondence, and $2,3,7$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lehmer's Problem, McKay's Correspondence, and $2,3,7$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-340425