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Quadratic Gauss Sums

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Quadratic Number Fields

Part of the book series: Springer Undergraduate Mathematics Series ((SUMS))

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Abstract

We introduce Pell forms and show they lead us in a natural way to quadratic Gauss sums. We point out connections to the analytic class number formula and the modularity of elliptic curves.

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Notes

  1. 1.

    See [26].

  2. 2.

    In the theory of complex multiplication there exists something called “the modular polynomial.”

  3. 3.

    I highly recommend the books [4, 5] to everyone interested in learning more about the big picture.

  4. 4.

    See Evink and Helminck [40].

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Authors and Affiliations

  1. Jagstzell, Germany

    Franz Lemmermeyer

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  1. Franz Lemmermeyer
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Lemmermeyer, F. (2021). Quadratic Gauss Sums. In: Quadratic Number Fields. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-78652-6_10

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