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More on Elliptic Fields

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The Riemann Hypothesis in Characteristic p in Historical Perspective

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

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Abstract

While Hasse worked on the RHp for elliptic fields he and his team discovered several properties of elliptic fields in characteristic p which were new and important although they were not absolutely necessary for the proof of RHp. In this chapter I am going to discuss some of them.

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Notes

  1. 1.

    The investigation of those polynomials for the supersingular invariants has produced a number of highly interesting papers, some of them connecting to the theory of modular forms. See, e.g., the list of references in [Mor06]. I would like to thank Patrick Morton for pointing out to me that those papers arose from the interest generated by Deuring’s paper. In particular the question of determining directly the number of roots of P(j) was solved, which Deuring could solve only indirectly by means of Eichler’s class number formula for quaternions [Eic37].

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  1. Mathematical Institute, Heidelberg University, Heidelberg, Germany

    Peter Roquette

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  1. Peter Roquette
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Roquette, P. (2018). More on Elliptic Fields. 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_8

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