Higher
rank?

•Like the moment problem, nothing is known about
infinitude of zeroes on the critical line for degree d > 2
L-functions.

•In fact, aside from
zeroes at s = 1/2 coming from algebraic geometry, it is not
known there are any zeroes on the critical line for

d > 2.

d > 2.

•Possible approach: if a
certain Fourier component of the automorphic distribution of a cusp
form t on GL(4,Z)nGL(4,R) vanishes to infinite order at 1, then L(1/2+it,t) = 0 for infinitely many t 2 R.