Taniyama

A book focusing on elliptic curves, beginning at an undergraduate level ( at least for those who have had a course on abstract algebra ), and progressing into much more advanced topics, even at the end touching on Andrew Wiles ' proof of the Taniyama – Shimura conjecture which led to the proof of Fermat's last theorem.

* Almost all the characters of Ghost Hunt like Taniyama Mai, Kazuya Shibuya and all the members of the SPR.

* In mathematics, the modularity theorem ( formerly the Taniyama – Shimura conjecture ) establishes a connection between elliptic curves and modular forms.

Taylor, together with Christophe Breuil, Brian Conrad, and Fred Diamond, completed the proof of the Taniyama – Shimura conjecture, by performing quite heavy technical computations in the case of additive reduction.

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.

This provided a bridge between Fermat and Taniyama by showing that a counterexample to Fermat's Last Theorem would create such a curve that would not be modular.

The conjecture attracted considerable interest when Frey ( 1986 ) suggested that the Taniyama – Shimura – Weil conjecture implies Fermat's Last Theorem.

In the summer of 1986, Ribet ( 1990 ) proved the epsilon conjecture, thereby proving that the Taniyama – Shimura – Weil conjecture implied Fermat's Last Theorem.

By the Taniyama – Shimura conjecture, E is a modular elliptic curve.

* Voiced by: Kisho Taniyama and Chiwa Saitō ( young ) ( Japanese ), Drew Aaron ( English )

In 1985 Frey pointed out a connection between Fermat's last theorem and the Taniyama conjecture, and this connection was made precise shortly thereafter by Kenneth Ribet, who proved that the Taniyama conjecture implies Fermat's last theorem.

Yutaka Taniyama ( Japanese: 谷山 豊 Taniyama Yutaka ; November 12, 1927, Kisai near Tokyo – November 17, 1958, Tokyo ) was a Japanese mathematician known for the Taniyama – Shimura conjecture.

Taniyama was best known for conjecturing, in modern language, automorphic properties of L-functions of elliptic curves over any number field.

A partial and refined case of this conjecture for elliptic curves over rationals is called the Taniyama – Shimura conjecture or the modularity theorem whose statement he subsequently refined in collaboration with Goro Shimura.

The names Taniyama, Shimura and Weil have all been attached to this conjecture, but the idea is essentially due to Taniyama.

In 1986 Ribet proved that if the Taniyama – Shimura conjecture held, then so would Fermat's last theorem, which inspired Andrew Wiles to work for a number of years in secrecy on it, and to prove enough of it to prove Fermat's Last Theorem.

Due to the pioneering contribution of Wiles and the efforts of a number of mathematicians the Taniyama – Shimura conjecture was finally proven in 1999.

The original Taniyama conjecture for elliptic curves over arbitrary number fields remains open, and the method of Wiles and others cannot be extended to provide its proof.

On November 17, 1958, Taniyama committed suicide.

Taniyama also mentioned in the note his concern that some might be harmed by his suicide and his hope that the act would not cast " a dark shadow over that person.

de: Yutaka Taniyama