We define a -adic character to be a continuous homomorphism from to . For , we use the ring of big Witt vectors over to exhibit a bijection between -adic characters and sequences of elements in , indexed by natural numbers relatively prime to , and for which . To such a -adic character we associate an -function, and we prove that this -function is -adic meromorphic if the corresponding sequence is overconvergent. If more generally the sequence is -convergent, we show that the associated -function is meromorphic in the open disk of radius . Finally, we exhibit examples of -convergent sequences with associated -functions which are not meromorphic in the disk of radius for any .
"-functions of -adic characters." Nagoya Math. J. 213 77 - 104, March 2014. https://doi.org/10.1215/00277630-2379114