Relating Mahler measures and Dirichlet $L$-values: new evidence for Chinburg's conjectures

David Hokken, Mahya Mehrabdollahei, Berend Ringeling

Let ${\chi }_{-f}$ be the odd quadratic Dirichlet character of conductor $f$, and let $\mathrm{m}(P)$ denote the Mahler measure of a polynomial $P$. In 1984, Chinburg conjectured that fo…