  In 1924 Littlewood showed that, assuming the Riemann Hypothesis, for large t
there is a constant C such that |\zeta(1/2+it)| \ll \exp(C\log t/\log \log t).
In this note we show how the problem of bounding |\zeta(1/2+it)| may be framed
in terms of minorizing the function \log ((4+x^2)/x^2) by functions whose
Fourier transforms are supported in a given interval, and drawing upon recent
work of Carneiro and Vaaler we find the optimal such minorant. Thus we
establish that any C> (\log 2)/2 is permissible in Littlewood's result.
