Factorisation of two-variable p-adic L-functions

Abstract

Let $f$ be a modular form which is non-ordinary at $p$. Kim and Loeffler have recently constructed two-variable $p$-adic $L$-functions associated to $f$. In the case where $a_p=0$, they showed that, as in the one-variable case, Pollack's plus and minus splitting applies to these new objects. In this short note, we show that such a splitting can be generalised to the case where $a_p\ne 0$ using Sprung's logarithmic matrix.

6 pages

References in corpus (2)

• P-adic integration on ray class groups and non-ordinary p-adic L-functions
• On pairs of p-adic analogues of the conjectures of Birch and Swinnerton-Dyer

Cited by in corpus (4)

• The Iwasawa Main Conjecture for elliptic curves at odd supersingular primes
• On pairs of p-adic L-functions for weight two modular forms
• Ranks of elliptic curves over Z_p^2-extensions
• Codimension two cycles in Iwasawa theory and elliptic curves with supersingular reduction