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novler
novler
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If I somehow know that for each elliptic curve over $\mathbb{Q}$ the $L$-function has a meromorphic continuation to the whole plane can I easily deduce modularity from that?

If not is there a way to establish meromorphic continuation without going through modularity?

If I somehow know that for each elliptic curve over $\mathbb{Q}$ the $L$-function has a meromorphic continuation to the whole plane can I easily deduce modularity from that?

If I somehow know that for each elliptic curve over $\mathbb{Q}$ the $L$-function has a meromorphic continuation to the whole plane can I easily deduce modularity from that?

If not is there a way to establish meromorphic continuation without going through modularity?

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novler
novler
  • 441
  • 2
  • 5

Does $L$-functions of elliptic curves over $\mathbb{Q}$ being meromorphic obviously imply modularity?

If I somehow know that for each elliptic curve over $\mathbb{Q}$ the $L$-function has a meromorphic continuation to the whole plane can I easily deduce modularity from that?