Timeline for Counting integral points on a surface
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 6, 2016 at 0:24 | answer | added | Stanley Yao Xiao | timeline score: 1 | |
| Nov 5, 2016 at 23:01 | comment | added | Fan Zheng | @StanleyYaoXiao That saved the day! Could you post this as an answer? Thank you very much! | |
| Nov 4, 2016 at 20:48 | comment | added | Stanley Yao Xiao | If $f$ is homogeneous and degree at least $2$, then Heath-Brown's 2002 Annals paper established that $N(f; B) = \# \{(x_1, x_2, x_3, x_4) \in \mathbb{Z}^4 : f(x_1, x_2, x_3, x_4) = , \max |x_i| \leq B\} = O_\epsilon(B^{2 + \epsilon})$. One can find examples (when $f$ is a quadratic form for instance) which shows that, in general, this is the best possible bound. Heath-Brown's theorem is also UNIFORM in $f$, meaning the implied constant in the big-$O$ does not depend on $f$. | |
| Nov 4, 2016 at 19:36 | history | asked | Fan Zheng | CC BY-SA 3.0 |