|
2 | deleted 27 characters in body; edited body; added 1 characters in body | ||
|
If $r_k(n)$ is the number of representations of $n$ as a sum of $k$ squares, and $k\geq 5$, then it is known that the estimate $\sum_{n \leq X}r_k(n)=C_k X^{\frac{k}{2}}+O(X^{\frac{k}{2}-1}\log{x})$X^{\frac{k}{2}}+O(X^{\frac{k}{2}-1})$ is known, and for $k\geq 4$ this is best possible, because $r_k(n) \neq O(n^{\frac{k}{2}-1})$ for $k\geq 4$ fixedo(n^{\frac{k}{2}-1})$. |
||||
|
|
1 |
|
||
|
If $r_k(n)$ is the number of representations of $n$ as a sum of $k$ squares, then it is known that $\sum_{n \leq X}r_k(n)=C_k X^{\frac{k}{2}}+O(X^{\frac{k}{2}-1}\log{x})$ and for $k\geq 4$ this is best possible, because $r_k(n) \neq O(n^{\frac{k}{2}-1})$ for $k\geq 4$ fixed. |
||||
