High Quality Content by WIKIPEDIA articles! In mathematics, Ribet's theorem (earlier called the epsilon conjecture or ?-conjecture) is a statement in number theory concerning properties of Galois representations associated with modular forms. It was proposed by Jean-Pierre Serre and proved by Ken Ribet. The proof of epsilon conjecture was a significant step towards the proof of Fermat's Last Theorem. As shown by Serre and Ribet, the Taniyama–Shimura conjecture (whose status was unresolved at the time) and the epsilon conjecture together imply that Fermat's Last Theorem is true. Ribet mentions in a NOVA program entitled "The Proof" that Barry Mazur casually assisted him in the completion of his proof by suggesting that he add a "gamma-zero of (M) structure" ( denoted ?0(m) , see modular group Gamma0 ) to generalize his results.

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