Modularity theorem: Difference between revisions

Revision as of 05:24, 2 June 2021

Revision as of 15:12, 30 June 2021

Line 26:

The modularity theorem implies a closely related analytic statement:

toTo aneach elliptic curve ''E'' over <math>\mathbf{Q}</math> we may attach a corresponding [[L-series of an elliptic curve|L-series]]. The <math>L</math>-series is a [[Dirichlet series]], commonly written

:<math>L(E, s) = \sum_{n=1}^\infty \frac{a_n}{n^s}.</math>