  We define an axiomatic class of L-functions extending the Selberg class. We
show in particular that one can recast the traditional conditions of an Euler
product, analytic continuation and functional equation in terms of
distributional identities akin to Weil's explicit formula. The generality of
our approach enables some new applications; for instance, we show that the
L-function of any cuspidal automorphic representation of GL_3(A_Q) has
infinitely many zeros of odd order.
