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Part of the book series: Progress in Mathematics ((PM,volume 26))

Abstract

Let K be a number field and let E/K be an elliptic curve.

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References

  1. B.J. Birch. “How the Number of Points of an Elliptic Curve over Fixed Prime Field Varies,” J. London Math. Soc. 43 (1968), 57–60.

    Google Scholar 

  2. P. Deligne. “La conjecture de Weil I,” Puhl. Math. IHES 43 (1974), 273–307.

    Google Scholar 

  3. P. Deligne. “La conjecture de Weil II,” Puhl. Math. IHES 52 (1980), 138–252.

    Google Scholar 

  4. L. Fejer. “Über trigonometrische Polynome,” J. Reine Angew. Math. ]46 (1916), 53–82.

    Google Scholar 

  5. E. Hecke. Mathematische Werke, Springer-Verlag, Göttingen, 1959.

    Google Scholar 

  6. J. Igusa. “Fibre Systems of Jacobian Varieties, III, Fibre Systems of Elliptic Curves,” Amer. J. Math. 8j_ (1959), 453–476.

    Google Scholar 

  7. S. Knapowski. “On a Theorem of Hecke,” J. Number Theory J_ (1969), 235–251.

    Google Scholar 

  8. B. Mazur. “Rational Points of Abelian Varieties with Values in Towers of Number Fields,” Invent. Math.S_ (1972), 183–266.

    Google Scholar 

  9. J. Milne. ßtale Cohomology, Princeton University Press, Princeton, 1980. (See also P. Deligne, SGA 4%, Lecture Notes in Mathematics 569, Springer-Verlag, Heidelberg, 1977 ).

    Google Scholar 

  10. A.P. Ogg. “A Remark on the Sato-Tate Conjecture,” Invent. Math. 9 (1970), 198–200.

    Article  Google Scholar 

  11. J.-P. Serre. Abelian l-adic Representation and Elliptic Curves, Benjamin, New York, 1968.

    Google Scholar 

  12. J. Täte. “Algebraic Cycles and Poles of Zeta Functions,” in: Arithmetical Algebraic fceometry, ( F.G. Schilling, ed.), Harper and Row, New York, 1965.

    Google Scholar 

  13. H. Yoshida. “An Analogue of the Sato Conjecture,” Invent. Math. 19 (1973), 261–277. Department of Mathematics Harvard University Cambridge, Massachusetts

    Google Scholar 

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© 1982 Springer Science+Business Media New York

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Murty, V.K. (1982). On the Sato-Tate Conjecture. In: Koblitz, N. (eds) Number Theory Related to Fermat’s Last Theorem. Progress in Mathematics, vol 26. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-6699-5_12

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  • DOI: https://doi.org/10.1007/978-1-4899-6699-5_12

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-0-8176-3104-8

  • Online ISBN: 978-1-4899-6699-5

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