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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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
M.D. Fried, M. Jarden, Field Arithmetic, 3rd edn. (Springer, Berlin, 2008), xiv+792 pp. Revised edn. by Moshe Jarden (2008)
E. Freitag, R. Kiehl, Étale Cohomology and the Weil Conjecture. With a Historical Introduction by J. A. Dieudonné (Springer, Berlin, 1988)
A. Grothendieck, Sur une note de Mattuck-Tate. J. Reine Angew. Math. 200, 208–215 (1958)
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)
A. Mattuck, J. Tate, On the inequality of Castelnuovo-Severi. Abh. Math. Semin. Univ. Hamburg 22, 295–299 (1958)
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)
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)
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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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DOI: https://doi.org/10.1007/978-3-319-99067-5_13
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