The problem of finding upper bounds for L-functions at the edge of the
critical strip has a long and interesting history. Here, the situation for
classical L-functions such as Dirichlet L-functions is relatively well
understood. The reason for this is because the size of the coefficients of
these L-functions is known to be small. Although L-functions are generally
expected to have coefficients which are bounded by a constant at the primes,
this has only been proven for a small class of familiar examples.