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‎Sur les fonctions algébriques à corps de constantes fini.‎

‎(Paris, Gauthier-Villars et Cie, 1940). 4to. Without wrappers. In: ""Comptes Rendus Hebdomadaires des Séances de L'Academie des Sciences"", Tome 210, No 17. Pp. (589-) 616. (Entire issue offered). Stamp on front page. Weil's paper: pp. 592-594.‎

‎First printing of Weil's importent paper in which he introduced the concept of Weil-pairing, giving a proof of the Riemann hypothesis for curves over finite fields.The Weil pairing is a pairing (bilinear form, though with multiplicative notation) on the points of order dividing n of an elliptic curve E, taking values in nth roots of unity. The Weil pairing is used in number theory and algebraic geometry, and has also been applied in elliptic curve cryptography and identity based encryption.""The Weil pairing, first introduced by André Weil in 1940, plays an important role in the theoretical study of the arithmetic of elliptic curves and Abelian varieties. It has also recently become extremely useful in cryptologic constructions related to those objects.""(Victor S. Miller).The Weil pairing is used in number theory and algebraic geometry, and has also been applied in elliptic curve cryptography and identity based encryption.‎