Timeline for How many integers below $n$ can be expressed as a sum of $k$ $m$th powers?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Jul 25, 2019 at 20:22 | comment | added | Christian Gaetz | For $m$ even you're certainly not going to get $\Theta(n)$ for small $k$. Since $m$-th powers are positive, there are at most $n^{1/m}$ possible summands, and so there are $O(n^{k/m})$ possible sums of $k$ $m$-th powers which are at most $n$. Thus your bound in the second bullet point can be improved a lot. | |
| Jul 25, 2019 at 18:40 | review | First posts | |||
| Jul 25, 2019 at 19:37 | |||||
| Jul 25, 2019 at 18:37 | history | asked | aras | CC BY-SA 4.0 |