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Factorisation of Two-variable p-adic L-functions

Published online by Cambridge University Press:  20 November 2018

Antonio Lei
Antonio Lei*
Affiliation:
Department of Mathematics and Statistics, Burnside Hall, McGill University, Montreal QC, H3A 0B9 e-mail: antonio.lei@mcgill.ca
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Abstract.

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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.

Keywords

11S4011S80modular formsp-adic L-functionssupersingular primes
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 4 , 01 December 2014 , pp. 845 - 852
Copyright
Copyright © Canadian Mathematical Society 2014

References

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