Pacific Journal of Mathematics

An elementary proof of the Riemann hypothesis for an elliptic curve over a finite field.

Horst G. Zimmer

Article information

Source
Pacific J. Math., Volume 36, Number 1 (1971), 267-278.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102971286

Mathematical Reviews number (MathSciNet)
MR0284442

Zentralblatt MATH identifier
0211.06702

Subjects
Primary: 14.47

Citation

Zimmer, Horst G. An elementary proof of the Riemann hypothesis for an elliptic curve over a finite field. Pacific J. Math. 36 (1971), no. 1, 267--278. https://projecteuclid.org/euclid.pjm/1102971286


Export citation

References

  • [1] M. Eichler, Introduction to the Theory of Algebraic Numbers and Functions, Acade- mic Press, New York and London, 1966.
  • [2] I. V. Elistratov, Elementaryproof of Hasse's theorem, Izdat. Saratov Univ., Saratov 1966, 21-26; MR 34 #4253 (1967).
  • [3] H. Hasse, Beweis des Analogous der RiemannschenVermutung fur die Artinschen und F. K. SchmidtschenKongruenzzetafunktionenin gewissen elliptischenFallen, Nachr. Ges. Wiss. Gottingen, Math.-Phys. Kl. I, 42 (1933), 253-262.
  • [4] H. Hasse, ZurTheorie der abstraktenelliptischen Funktionenkorper,J. Reine Angew. Math. 175 (1936), 55-62, 69-88, 193-208.
  • [5] E. Lutz, Sur I'equation y2 = x* -- Ax -- B dans les corps p-adiques, J. Reine Angew. Math. 177 (1937), 238-244.
  • [6] Ju. I. Manin, On cubic congruences to a prime modulus, Izv. Akad. Nauk SSSR, Mat. Ser. 20 (1956), 673-678; or Amer. Math. Soc. Trans. (2) 13 (1960), 1-7; MR 18 380 (1957).