Extreme values of zeta and L-functions

We introduce a "resonance" method to produce large values of $|\zeta(1/2+it)|$ and large and small central values of $L$-functions.Comment: 16 pages; Version 2 makes a few light revisions. To appear in Math. Annale

Nonvanishing of quadratic Dirichlet L-functions at s=1/2

We show that for a positive proportion of fundamental discriminants d, L(1/2,chi_d) != 0. Here chi_d is the primitive quadratic Dirichlet character of conductor d.Comment: 42 pages, published versio