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L-functions of p-adic characters

Published online by Cambridge University Press:  11 January 2016

Christopher Davis and
Daqing Wan
Christopher Davis*
Affiliation:
Department of Mathematics University of California, Irvine, Irvine, California 92697, USA
Daqing Wan
Affiliation:
Department of Mathematics University of California, Irvine, Irvine, California 92697, USA, dwan@math.uci.edu
*
University of Copenhagen Department of Mathematical Sciences, Universitetsparken 5 2100 København Ø, Denmark, davis@math.ku.dk
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Abstract

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We 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.

Keywords

11G4013F35

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 213 , March 2014, pp. 77 - 104
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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