Besides its role in proving Fermat's Last Theorem and its well-known consequence that the $L$-function of an elliptic curve is defined at 1 (so that, in particular, the BSD Conjecture makes sense), what are the other applications of the Modularity Theorem? Wikipedia cites one: the sum of coprime $n$th powers can never be a cube, but gives no reference. I am after as many consequences as you all can provide, as I will be compiling them to present to a seminar this summer.
2026-04-02 23:45:56.1775173556
Applications of the Modularity Theorem
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