For any rational number
, define
the logarithmic Martinet function
to be the liminf of the logarithm of the root discriminant of number fields
with
as
goes to infinity. Under the generalized Riemann hypothesis
for Dedekind zeta functions of number fields, we show that
for a dense subset
of rational numbers
.
We also study unconditional estimates of the growth of root discriminants by
studying how the polynomial discriminant behaves under perturbation of coefficients,
and by using Pisot numbers.
Keywords
Chebotarev density theorem, class field towers, Pisot
numbers, root discriminants