English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper is mainly concerned with identities like \[ (x_1^d + x_2^d +\cdots + x_r^d) (y_1^d + y_2^d + \cdots y_n^d) = z_1^d + z_2^d + \cdots + z_n^d\] where $d>2,$ $x=(x_1, x_2, \dots, x_r)$ and $y=(y_1, y_2, \dots, y_n)$ aresystems of indeterminates and each $z_k$ is a linear form in $y$ withcoefficients in the rational function field $\k (x)$ over any field $\k$ ofcharacteristic $0$ or greater than $d.$ These identities are higher degreeanalogue of the well-known composition formulas of sums of squares of Hurwitz,Radon and Pfister. We show that such composition identities of sums of powersof degree at least $3$ are trivial, i.e., if $d>2,$ then $r=1.$ Our proof issimple and elementary, in which the crux is Harrison's center theory ofhomogeneous polynomials.

Harrison center and products of sums of powers