We describe a possible alternative to the explicit formula and give two applications. The first relates the maximum of the Riemann zeta function on the one-line (and in the critical strip) to the maximum of S(t) - the remainder in the formula for the number of non-trivial zeros of height t. The second is concerned with cancellations of the Mobius function. In particular, we give new conditional upper bounds for partial sums of the Mobius function.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/246