An elementary approach to L-functions mod p

We give a brief presentation of basic facts concerning the relationship of L-functions mod p and the Cartier operator. We take the notion of the Carri er operator For granted but develop all other notions thar we need From scr atch. An idea taken from Tate's famous "sum of residues equals zero" paper plays a key role and gives the payer a distinctly "functional analytic" fla vor. All the ideas in the paper have been "in the air" for some time; our c ontribution is simply to organize them and to express them succinctly. (C) 2000 Academic Press.