LARGE GREATEST COMMON DIVISOR SUMS AND EXTREME VALUES OF THE RIEMANN ZETA FUNCTION

It is shown that the maximum of vertical bar zeta(1/2 + it)vertical bar on the interval T-1/2 <= t <= T is at least exp((1/root 2+o(1) root logT log log log T/log log T). Our proof uses Soundararajan's resonance method and a certain large greatest common divisor sum. The method of proof shows that the absolute constant A in the inequality sup(1 <= n1<...