P-adic integration on ray class groups and non-ordinary p-adic L-functions
Number Theory
2015-12-15 v3
Abstract
We study the theory of finite-order p-adic functions and distributions on ray class groups of number fields, and apply this to the construction of (possibly unbounded) p-adic L-functions for automorphic forms on GL(2) which may be non-ordinary at the primes above p. As a consequence, we obtain a "plus-minus" decomposition of the p-adic L-functions of automorphic forms for GL(2) over an imaginary quadratic field with p split and Hecke eigenvalues 0 at the primes above p, confirming a conjecture of B.D. Kim.
Cite
@article{arxiv.1304.4042,
title = {P-adic integration on ray class groups and non-ordinary p-adic L-functions},
author = {David Loeffler},
journal= {arXiv preprint arXiv:1304.4042},
year = {2015}
}
Comments
Revised version correcting some errors in the interpolation formulae