P-adic integration on ray class groups and non-ordinary p-adic L-functions

TL;DR

This paper develops a p-adic integration framework on ray class groups to construct p-adic L-functions for automorphic forms, including non-ordinary cases, and confirms a conjecture related to their decomposition over imaginary quadratic fields.

Contribution

It introduces a novel approach to p-adic L-functions for non-ordinary automorphic forms using p-adic distributions on ray class groups, extending previous theories.

Findings

Constructed p-adic L-functions for non-ordinary automorphic forms.

Established a plus-minus decomposition for these L-functions.

Confirmed B.D. Kim's conjecture on the decomposition in specific cases.

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.