We prove Khinchin-type inequalities with sharp constants for type L random variables and all even moments. Our main tool is Hadamards factorisation theorem from complex analysis, combined with Newtons inequalities for elementary symmetric functions. Besides the case of independent summands, we also treat ferromagnetic dependencies in a nonnegative external magnetic field (thanks to Newmans 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.
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