Factorisation of Two-variablep-adicL-functions

Abstract

Abstract.Letfbe a modular form that is non-ordinary atp. Loeffler has recently constructed four two-variablep-adicL-functions associated withf. In the case whereap= 0, he showed that, as in the one-variable case, Pollack’s plus and minus splitting applies to these new objects. In this article, we show that such a splitting can be generalised to the case whereap≠ 0 using Sprung’s logarithmic matrix.