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Search: All articles in the CMB digital archive with keyword L-function

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1. CMB Online first

Lei, Antonio
Factorisation of Two-variable $p$-adic $L$-functions
Let $f$ be a modular form which is non-ordinary at $p$. Loeffler has recently constructed four two-variable $p$-adic $L$-functions associated to $f$. 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 $a_p\ne0$ using Sprung's logarithmic matrix.

Keywords:modular forms, p-adic L-functions, supersingular primes
Categories:11S40, 11S80

2. CMB 2013 (vol 57 pp. 381)

Łydka, Adrian
On Complex Explicit Formulae Connected with the Möbius Function of an Elliptic Curve
We study analytic properties function $m(z, E)$, which is defined on the upper half-plane as an integral from the shifted $L$-function of an elliptic curve. We show that $m(z, E)$ analytically continues to a meromorphic function on the whole complex plane and satisfies certain functional equation. Moreover, we give explicit formula for $m(z, E)$ in the strip $|\Im{z}|\lt 2\pi$.

Keywords:L-function, Möbius function, explicit formulae, elliptic curve
Categories:11M36, 11G40

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