Year: 2026
Type: preprint
Abstract: We prove a conjecture of Smyth on the Mahler measure of non-reciprocal trinomials of height $1$, determining exactly when their Mahler measures are greater than or less than $M(x+y+1)=ρ=1.381356\ldots$, conjectured to be the smallest limit point of $M(P)$ for non-reciprocal polynomials. Conjecturally, our result gives the full spectrum of $M(P)<ρ$ for all non-reciprocal polynomials, not just for trinomials.
Source: arXiv (Cornell University)
Author: Voutier, Paul M
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214966412