Ihara's growth conjecture for Euler–Kronecker constants of cyclotomic fields

For $m$ sufficiently large, let ${\mathbb Q}(\zeta_m)$ denote the $m$-th cyclotomic field and let $\gamma_{{\mathbb Q}(\zeta_m)}$ be its Euler–Kronecker constant. Ihara's growth conjecture. There are positive constants $0<a_0,a_1\leq 2$ such that, for every $\epsilon>0$,

$$(a_0-\epsilon)\log m<\gamma_{{\mathbb Q}(\zeta_m)}<(a_1+\epsilon)\log m.$$

The conjecture predicts logarithmic-order growth with positive lower and upper constants. The source later reports that results of Ford, Luca and Moree show that $\gamma_{{\mathbb Q}(\zeta_m)}$ can be negative, so the stated lower bound is refuted.