Skip to main content
Open Access Publications from the University of California

L-functions of p-ADIC characters

  • Author(s): Davis, C
  • Wan, D
  • et al.

We define a p-adic character to be a continuous homomorphism from 1 + tFq[[t]] to ℤ*p. For p > 2, we use the ring of big Witt vectors over Fqto exhibit a bijection between p-adic characters and sequences (ci)(i,p)=1 of elements in ℤq, indexed by natural numbers relatively prime to p, and for which limi→ci= 0. 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+εfor any ε > 0. © 2014 by The Editorial.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Main Content
Current View