L-functions of p-adic characters

Abstract

AbstractWe define a p-adic character to be a continuous homomorphism from For p > 2, we use the ring of big Witt vectors over to exhibit a bijection between p-adic characters and sequences (ci)(i,p)=1 of elements in indexed by natural numbers relatively prime to p, and for which . To such a p-adic character we associate an L-function, and we prove that this L-function is p-adic meromorphic if the corresponding sequence (ci) is overconvergent. If more generally the sequence is C log-convergent, we show that the associated L-function is meromorphic in the open disk of radius qC. Finally, we exhibit examples of C log-convergent sequences with associated L-functions which are not meromorphic in the disk of radius qC+∊ for any ∊ > 0.