  We prove Khinchin-type inequalities with sharp constants for type L random
variables and all even moments. Our main tool is Hadamard's factorisation
theorem from complex analysis, combined with Newton's inequalities for
elementary symmetric functions. Besides the case of independent summands, we
also treat ferromagnetic dependencies in a nonnegative external magnetic field
(thanks to Newman's generalisation of the Lee-Yang theorem). Lastly, we compare
the notions of type L, ultra sub-Gaussianity (introduced by Nayar and
Oleszkiewicz) and strong log-concavity (introduced by Gurvits), with the latter
two being equivalent.
