Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 213 (2014), 77-104.
-functions of -adic characters
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 .
Nagoya Math. J., Volume 213 (2014), 77-104.
First available in Project Euclid: 31 October 2013
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Davis, Christopher; Wan, Daqing. $L$ -functions of $p$ -adic characters. Nagoya Math. J. 213 (2014), 77--104. doi:10.1215/00277630-2379114. https://projecteuclid.org/euclid.nmj/1383240638