Sum of squares length of real forms


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SCHEIDERER, Claus, 2017. Sum of squares length of real forms. In: Mathematische Zeitschrift. 286(1-2), pp. 559-570. ISSN 0025-5874. eISSN 1432-1823

@article{Scheiderer2017squar-39241, title={Sum of squares length of real forms}, year={2017}, doi={10.1007/s00209-016-1773-z}, number={1-2}, volume={286}, issn={0025-5874}, journal={Mathematische Zeitschrift}, pages={559--570}, author={Scheiderer, Claus} }

<rdf:RDF xmlns:rdf="" xmlns:bibo="" xmlns:dc="" xmlns:dcterms="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dcterms:issued>2017</dcterms:issued> <dcterms:title>Sum of squares length of real forms</dcterms:title> <dc:language>eng</dc:language> <dcterms:abstract xml:lang="eng">For n,d≥1 let p(n, 2d) denote the smallest number p such that every sum of squares of degree d forms in R[x1,…,xn] is a sum of p squares. We establish lower bounds for p(n, 2d) that are considerably stronger than the bounds known so far. Combined with known upper bounds they give p(3,2d)∈{d+1,d+2} in the ternary case. Assuming a conjecture of Iarrobino–Kanev on dimensions of tangent spaces to catalecticant varieties, we show that p(n,2d)∼const⋅d(n−1)/2 for d→∞ and all n≥3. For ternary sextics and quaternary quartics we determine the exact value of the invariant, showing p(3,6)=4 and p(4,4)=5.</dcterms:abstract> <bibo:uri rdf:resource=""/> <dcterms:available rdf:datatype="">2017-06-13T09:14:58Z</dcterms:available> <dc:date rdf:datatype="">2017-06-13T09:14:58Z</dc:date> <dc:creator>Scheiderer, Claus</dc:creator> <dc:contributor>Scheiderer, Claus</dc:contributor> </rdf:Description> </rdf:RDF>

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