L-functions of p-adic characters

TY - JOUR

T1 - L-functions of p-adic characters

AU - Davis, Christopher James

AU - Wan, Daqing

PY - 2014/3

Y1 - 2014/3

N2 - 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 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 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+ε for any ε > 0.

AB - 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 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 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+ε for any ε > 0.

U2 - 10.1215/00277630-2379114

DO - 10.1215/00277630-2379114

M3 - Journal article

SN - 0027-7630

VL - 213

SP - 77

EP - 104

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

ER -