Timeline for Statements generalizing representability of integers by binary quadratic forms to $n$-variable higher homogeneous forms?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 7, 2015 at 6:31 | comment | added | user76479 | @WillSawin Would you by any chance know any similar statements and references? | |
| Sep 7, 2015 at 3:03 | comment | added | Will Sawin | @StanleyYaoXiao Isn't that only for rational numbers, not integral? | |
| Sep 5, 2015 at 22:24 | comment | added | user76479 | @individ I think representing prime numbers would be a good start if one can also give associated composition laws. | |
| Sep 5, 2015 at 22:22 | comment | added | user76479 | @StanleyYaoXiao Could you elaborate your idea? | |
| Sep 1, 2015 at 6:03 | comment | added | individ | You can think of a lot of ideas. Better more clearly define the issue. For example what kind of numbers required. Although this form can always lead to the Pell equation. | |
| Sep 1, 2015 at 0:58 | comment | added | user76479 | Pretty cool however I am not familiar with results you are talking about? Could you pleaase post a full address of details? | |
| Aug 31, 2015 at 22:59 | comment | added | Stanley Yao Xiao | The obvious generalization is to $n$-ary quadratic forms. They still satisfy the Hasse principle, as shown by Hasse-Minkowski. In general, the circle method can deal with degree $d$ forms as long as $n$ is large with respect to $d$ (see for example the seminal work of Birch). Another generalization is to norm-form equations; here the observation is that binary quadratic forms are norm forms for quadratic field extensions of the rationals. | |
| Aug 31, 2015 at 22:55 | history | asked | user76479 | CC BY-SA 3.0 |