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Search: MSC category 11G40 ( $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10] )

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1. CMB Online first

Loeffler, David
A note on $p$-adic Rankin-Selberg $L$-functions
We prove an interpolation formula for the values of certain $p$-adic Rankin-Selberg $L$-functions associated to non-ordinary modular forms.

Keywords:$p$-adic $L$-function, Iwasawa theory
Categories:11F85, 11F67, 11G40, 14G35

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

3. CMB 2007 (vol 50 pp. 486)

Cynk, S.; Hulek, K.
Higher-Dimensional Modular\\Calabi--Yau Manifolds
We construct several examples of higher-dimensional Calabi--Yau manifolds and prove their modularity.

Categories:14G10, 14J32, 11G40

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