On the p-adic L-function of Hilbert modular forms at supersingular primes

Abstract

In this paper, I discuss the construction of the p-adic L-function attached to a Hilbert modular form f, supersingular or ordinary, which turns out to be the non-archimedean Mellin transform of an h-admissible measure. And h is explicitly given. As a special case, when the Fourier coefficient of f at p|p is zero, plus/minus p-adic L-functions are furthermore defined as bounded functions, and they interpolate special values of L(f,χ,s) for cyclotomic characters χ. This can be used to formulate Iwasawa main conjecture for supersingular elliptic curve defined over a totally real field.