## A History of Abstract Algebra

Hiroshima Math. Abstract Article info and citation First page References See also Abstract We introduce two notions of equivalence for rational quadratic forms. Article information Source Hiroshima Math. Export citation.

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Export Cancel. References E. Beltrami, Saggio di interpretazione della geometria non-euclidea, Gior.

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- Arithmetic of Quadratic Forms : Goro Shimura : !

Beltrami, Teoria fondamentale degli spazii di curvatura constante, Annali di Mat. Serie II, 2 , Bianchi, Ricerche sulle forme quaternarie quadratiche e sui gruppi poliedrici, Annali di Matematica Pura e applicata 2 , 21 , Bianchi, Complemento alle ricerche sulle forme quaternarie quadratiche e sui gruppi poliedrici, Annali di Matematica Pura e applicata 2 , 23 , This work provided examples for which the equivalence between motivic and automorphic L -functions postulated in the Langlands program could be tested: automorphic forms realized in the cohomology of a Shimura variety have a construction that attaches Galois representations to them.

In , Shimura generalized the initial work of Martin Eichler on the Eichler—Shimura congruence relation between the local L -function of a modular curve and the eigenvalues of Hecke operators.

## NUMBER THEORY BOOKS, OR BEFORE

In , Shimura's work on explicit class field theory in the spirit of Kronecker's Jugendtraum resulted in his proof of Shimura's reciprocity law. Shimura's formulation of the Taniyama—Shimura conjecture later known as the modularity theorem in the s played a key role in the proof of Fermat's Last Theorem by Andrew Wiles in In , Kenneth Ribet proved Ribet's theorem which demonstrated that Fermat's Last Theorem followed from the semistable case of this conjecture.

His hobbies were shogi problems of extreme length and collecting Imari porcelain. Images, videos and audio are available under their respective licenses. Home FAQ Contact.

Goro Shimura Wikipedia open wikipedia design. Japanese mathematician.

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This article uses Western name order when mentioning individuals. Hamamatsu, Japan. Princeton , New Jersey.

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Princeton University Department of Mathematics. Retrieved 3 May Retrieved 9 May The Asahi Shimbun Company. Retrieved 4 May The Map of My Life Hardcover ed. Berlin: Springer-Verlag.