Lehmer’s Mahler measure constant

Upper bound, last-listed row

| $1.176280\ldots$ | [BDM2007] [Leh1933] | The value $1.176280\ldots$ (the Mahler measure of $\ell$) “remains the smallest known measure $>1$ for an integer polynomial,” i.e. it is the best currently known explicit upper bound for $L$. [BDM2007-smallest-known] |

exact pinned row

| $1.176280\ldots$ | <a href="#BDM2007">[BDM2007]</a> <a href="#Leh1933">[Leh1933]</a> | The value $1.176280\ldots$ (the Mahler measure of $\ell$) “remains the smallest known measure $>1$ for an integer polynomial,” i.e. it is the best currently known explicit upper bound for $L$. <a href="#BDM2007-smallest-known">[BDM2007-smallest-known]</a> |

tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $1$ | Trivial (Kronecker) | For $f\in\mathbb{Z}[x]$, one has $M(f)\ge 1$, with $M(f)=1$ precisely in the cyclotomic/monomial case; hence $L\ge 1$. [BDM2007-kronecker] |

exact pinned row

| $1$ | Trivial (Kronecker) | For $f\in\mathbb{Z}[x]$, one has $M(f)\ge 1$, with $M(f)=1$ precisely in the cyclotomic/monomial case; hence $L\ge 1$. <a href="#BDM2007-kronecker">[BDM2007-kronecker]</a> |

tracked since 2026-07-24 — no movement seen yet