Questions tagged [l-functions]

I have a problem to see how the galois-theoretic definition of the L-function of an elliptic curve gives the right answer and also the connection between the L-function of a weight 2 Hecke eigenform and the corresponding elliptic curve. Let E over…

In the introduction of this paper, the authors say that: Let $M \in \mathbb{Z}_{>0}$. If $f$ is a normalised newform for $\Gamma_0(M)$ then we define $$\Lambda(s,f)=(2\pi)^{-s}\Gamma(s) M^{s/2}L(s,f)$$ It satisfies a functional equation $$…