An elementary approach to L-functions mod p

We give a brief presentation of basic facts concerning the relationship of L-functions modp and the Cartier operator. We take the notion of the Cartier operator for granted but develop all other notions that we need from scratch. An idea taken from Tate's famous "sum of residues equals zero" paper plays a key role and gives the paper a distinctly "functional analytic" flavor. All the ideas in the paper have been "in the air" for some time; our contribution is simply to organize them and to express them succinctly.