Rocky Mountain Journal of Mathematics

A supplement to Manin's proof of the Hasse inequality

Jasbir S. Chahal, Afzal Soomro, and Jaap Top

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Abstract

In 1956 Yu.I.~Manin published an elementary proof of Helmut Hasse's 1933 result stating that the Riemann hypothesis holds in the case of an elliptic function field over a finite field. We briefly explain how Manin's proof relates to more modern proofs of the same result. This enables us to present an analogous elementary proof for the case of finite fields of characteristic two, which was excluded in the original argument.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 5 (2014), 1457-1470.

Dates
First available in Project Euclid: 1 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1420071550

Digital Object Identifier
doi:10.1216/RMJ-2014-44-5-1457

Mathematical Reviews number (MathSciNet)
MR3295638

Zentralblatt MATH identifier
1316.11054

Citation

Chahal, Jasbir S.; Soomro, Afzal; Top, Jaap. A supplement to Manin's proof of the Hasse inequality. Rocky Mountain J. Math. 44 (2014), no. 5, 1457--1470. doi:10.1216/RMJ-2014-44-5-1457. https://projecteuclid.org/euclid.rmjm/1420071550


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