On Leopoldt's and Gross's defects for Artin representations

We generalize Waldschmidt's bound for Leopoldt's defect and prove a similar bound for Gross's defect for an arbitrary extension of number fields. As an application, we prove new cases of the generalized Gross conjecture (also known as the Gross-Kuz'min conjecture) beyond the classical abelian case, and we show that Gross's p-adic regulator has at least half of the conjectured rank. We also describe and compute non-cyclotomic analogues of Gross's defect.