Open Access
March 2014 L-functions of p-adic characters
Christopher Davis, Daqing Wan
Nagoya Math. J. 213: 77-104 (March 2014). DOI: 10.1215/00277630-2379114


We define a p-adic character to be a continuous homomorphism from 1+tFq[[t]] to Zp. For p>2, we use the ring of big Witt vectors over Fq to 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 lim ici=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 Clog-convergent, we show that the associated L-function is meromorphic in the open disk of radius qC. Finally, we exhibit examples of Clog-convergent sequences with associated L-functions which are not meromorphic in the disk of radius qC+ϵ for any ϵ>0.


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Christopher Davis. Daqing Wan. "L-functions of p-adic characters." Nagoya Math. J. 213 77 - 104, March 2014.


Published: March 2014
First available in Project Euclid: 31 October 2013

zbMATH: 1292.11074
MathSciNet: MR3290686
Digital Object Identifier: 10.1215/00277630-2379114

Primary: 11G40
Secondary: 13F35

Rights: Copyright © 2014 Editorial Board, Nagoya Mathematical Journal

Vol.213 • March 2014
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