ECCC-Report TR24-026https://eccc.weizmann.ac.il/report/2024/026Comments and Revisions published for TR24-026en-usWed, 15 May 2024 17:12:23 +0300
Revision 1
| A subquadratic upper bound on sum-of-squares composition formulas |
Pavel Hrubes
https://eccc.weizmann.ac.il/report/2024/026#revision1For every $n$, we construct a sum-of-squares identitity
\[ (\sum_{i=1}^n x_i^2) (\sum_{j=1}^n y_j^2)= \sum_{k=1}^s f_k^2\,,\]
where $f_k$ are bilinear forms with complex coefficients and $s= O(n^{1.62})$. Previously, such a construction was known with $s=O(n^2/\log n)$.
The same bound holds over any field of positive characteristic.Wed, 15 May 2024 17:12:23 +0300https://eccc.weizmann.ac.il/report/2024/026#revision1
Paper TR24-026
| A subquadratic upper bound on sum-of-squares compostion formulas |
Pavel Hrubes
https://eccc.weizmann.ac.il/report/2024/026For every $n$, we construct a sum-of-squares identitity
\[ (\sum_{i=1}^n x_i^2) (\sum_{j=1}^n y_j^2)= \sum_{k=1}^s f_k^2\,,\]
where $f_k$ are bilinear forms with complex coefficients and $s= O(n^{1.62})$. Previously, such a construction was known with $s=O(n^2/\log n)$.
The same bound holds over any field of positive characteristic.Thu, 15 Feb 2024 14:10:21 +0200https://eccc.weizmann.ac.il/report/2024/026