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

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.

Revised version correcting some errors in the interpolation formulae

Cited by in corpus (11)

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• Factorisation of two-variable p-adic L-functions
• P-adic L-functions for GL(2)
• Interpolation of Generalized Heegner Cycles in Coleman Families
• $p$-adic heights of Heegner points and Beilinson-Flach elements
• Functional Equation for p-adic Rankin-Selberg L-functions
• Codimension two cycles in Iwasawa theory and elliptic curves with supersingular reduction
• On the algebraic functional equation for the mixed signed Selmer group over multiple ${\mathbb{Z}}_p$-extensions
• On $p$-adic $L$-functions for symplectic representations of GL(N) over number fields