eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-07-15
12:1
12:11
10.4230/LIPIcs.CCC.2024.12
article
A Subquadratic Upper Bound on Sum-Of-Squares Composition Formulas
Hrubeš, Pavel
1
https://orcid.org/0000-0003-4526-4934
Institute of Mathematics of ASCR, Prague, Czech Republic
For every n, we construct a sum-of-squares identity (∑_{i=1}^n x_i²) (∑_{j=1}^n y_j²) = ∑_{k=1}^s f_k², where f_k are bilinear forms with complex coefficients and s = O(n^1.62). Previously, such a construction was known with s = O(n²/log n). The same bound holds over any field of positive characteristic.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol300-ccc2024/LIPIcs.CCC.2024.12/LIPIcs.CCC.2024.12.pdf
Sum-of-squares composition formulas
Hurwitz’s problem
non-commutative arithmetic circuit