The Klein Quartic in Number Theory
| Title: | The Klein Quartic in Number Theory |
| Author: | Elkies, Noam |
| Citation: | Elkies, Noam D. The Klein quartic in number theory. In The Eightfold Way: The Beauty of Klein's Quartic Curve, ed. Sylvio Levi, 51-102. Mathematical Sciences Research Institute publications, 35. Cambridge: Cambridge University Press. |
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| Abstract: | We describe the Klein quartic X and highlight some of its remarkable properties that are of particular interest in number theory. These include extremal properties in characteristics 2, 3, and 7, the primes dividing the order of the automorphism group of X; an explicit identification of with the modular curve X(7); and applications to the class number 1 problem and the case n= 7 of Fermat. |
| Published Version: | http://www.msri.org/publications/books/Book35/contents.html |
| Terms of Use: | This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA |
| Citable link to this page: | http://nrs.harvard.edu/urn-3:HUL.InstRepos:2920120 |
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