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Appendix

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Part of the book series: Lecture Notes in Mathematics ((HISTORYMS,volume 2222))

Abstract

With the appearance of Weil’s above mentioned three books, the RHp was settled and our story comes to an end. But the mathematical development inspired by this or that item of our story persists and is still present. From the numerous literature in this direction I will mention here three papers only:

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Notes

  1. 1.

    And much more.

  2. 2.

    Added in proof: I am indebted to Franz Lemmermeyer for pointing out to me the recent papers [Mil16, OS16].

References

  1. E. Bombieri, Counting points on curves over finite fields (d’apres S.A. Stepanov), Sem. Bourbaki 1972/1973. Expose No. 430, Lecture Notes in Mathematics, vol. 383 (Springer, Berlin, 1974), pp. 234–241

    Google Scholar 

  2. M.D. Fried, M. Jarden, Field Arithmetic, 3rd edn. (Springer, Berlin, 2008), xiv+792 pp. Revised edn. by Moshe Jarden (2008)

    Google Scholar 

  3. E. Freitag, R. Kiehl, Étale Cohomology and the Weil Conjecture. With a Historical Introduction by J. A. Dieudonné (Springer, Berlin, 1988)

    Chapter  Google Scholar 

  4. A. Grothendieck, Sur une note de Mattuck-Tate. J. Reine Angew. Math. 200, 208–215 (1958)

    MathSciNet  MATH  Google Scholar 

  5. J.S. Milne, The Riemann hypothesis over finite fields - from Weil to the present day, in The Legacy of Bernhard Riemann After One Hundred and Fifty Years, vol. II (International Press Somerville, MA, 2016), pp. 487–565; (Higher Education Press, Beijing, 2016)

    Article  MathSciNet  Google Scholar 

  6. A. Mattuck, J. Tate, On the inequality of Castelnuovo-Severi. Abh. Math. Semin. Univ. Hamburg 22, 295–299 (1958)

    Article  MathSciNet  Google Scholar 

  7. F. Oort, N. Schappacher, Early history of the Riemann hypothesis in positive characteristic, in The Legacy of Bernhard Riemann After One Hundred and Fifty Years, vol. II (International Press, Somerville, MA, 2016), pp. 595–631; (Higher Education Press, Beijing, 2016)

    Google Scholar 

  8. S.A. Stepanov, Über die Anzahl der Punkte einer hyperelliptischen Kurve über einem einfachen endlichen Körper. Izv. Akad. Nauk SSSR, Ser. Mat. 33, 1171–1181 (1969)

    Google Scholar 

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Roquette, P. (2018). Appendix. In: The Riemann Hypothesis in Characteristic p in Historical Perspective. Lecture Notes in Mathematics(), vol 2222. Springer, Cham. https://doi.org/10.1007/978-3-319-99067-5_13

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