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Factorisation of Two-variable p-adic L-functions
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- Journal:
- Canadian Mathematical Bulletin / Volume 57 / Issue 4 / 01 December 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 845-852
- Print publication:
- 01 December 2014
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- Article
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Let
$f$ be a modular form that is non-ordinary at 
$p$. Loeffler has recently constructed four two-variable $p$-adic 
$L$-functions associated with $f$. In the case where 
${{a}_{p}}\,=\,0$, 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 where 
${{a}_{p}}\ne 0$ using Sprung’s logarithmic matrix.
