P-Adic Integration on Ray Class Groups and Non-ordinary p-Adic L-Functions

Abstract

We study the theory of p-adic finite-order 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 \(\mathop{\text{GL}}\nolimits _{2}\) 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 \(\mathop{\text{GL}}\nolimits _{2}\) over an imaginary quadratic field with p split and Hecke eigenvalues 0 at the primes above p, confirming a conjecture of B.D. Kim.KeywordsModular FormNumber FieldAutomorphic FormOpen SubgroupAutomorphic RepresentationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.