Timeline for Solutions to the Diophantine equation $x^2+3y^2+3z^2=n$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 5, 2018 at 17:52 | comment | added | John Voight | For the modular forms proof, the fact of class number one translates into no cusp forms, and then the local calculation is the determination the precise (linear combination of) Eisenstein series. | |
| Jul 5, 2018 at 17:50 | comment | added | John Voight | You're most welcome, and please call me John! Let me know if you have any comments or questions (on anything in the book!). Of course, I have a slight quaternionic bias, but you can also do all of this (equivalently) in the language of ternary quadratic forms: Siegel has given an expression for the average number of representations over the genus, and the fact that there is only one class in the genus for each of your ternary quadratic forms means you have a formula. There is again a "local mass" (equivalent to the local embedding numbers). | |
| Jul 4, 2018 at 1:29 | comment | added | Anton | Thanks for the response, Prof. Voight! I learned the basics of quaternion algebras from your book, as well as from the lecture notes of M.F. Vignéras. Will take a look at the theorems you referenced. P.S. Thank you very much for your fundamental monograph! | |
| Jul 4, 2018 at 1:12 | vote | accept | Anton | ||
| Jul 3, 2018 at 23:12 | history | answered | John Voight | CC BY-SA 4.0 |