Download E-books Elliptic Curves. (MN-40) PDF

By Anthony W. Knapp

An elliptic curve is a selected type of cubic equation in variables whose projective options shape a gaggle. Modular varieties are analytic services within the top part aircraft with definite transformation legislation and development houses. the 2 subjects--elliptic curves and modular forms--come jointly in Eichler-Shimura idea, which constructs elliptic curves out of modular varieties of a unique type. The speak, that each one rational elliptic curves come up this manner, is named the Taniyama-Weil Conjecture and is understood to suggest Fermat's final Theorem.

Elliptic curves and the modeular varieties within the Eichler- Shimura idea either have linked L services, and it's a outcome of the speculation that the 2 varieties of L capabilities fit. the speculation lined by means of Anthony Knapp during this booklet is, for this reason, a window right into a huge expanse of mathematics--including category box idea, mathematics algebraic geometry, and team representations--in which the concidence of L services relates research and algebra within the so much basic ways.

Developing, with many examples, the easy concept of elliptic curves, the publication is going directly to the topic of modular kinds and the 1st connections with elliptic curves. The final chapters obstacle Eichler-Shimura idea, which establishes a far deeper courting among the 2 matters. No different booklet in print treats the elemental concept of elliptic curves with in basic terms undergraduate arithmetic, and no different explains Eichler-Shimura conception in such an available manner.

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