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Home > Research > Publications & Outputs > The number of zeros of a sum of fractional powers.
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The number of zeros of a sum of fractional powers.

Research output: Contribution to journalJournal article

Published

Journal publication date8/06/2006
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Journal number2070
Volume462
Number of pages10
Pages1821-1830
Original languageEnglish

Abstract

We consider functions of the form f(x=∑j=1ncjx+ajp, where where a1>c⃛>an≥0. A version of Descartes's rule of signs applies. Further, if Cj=∑i=1jci and Cn=0, then the number of zeros of f is bounded by the number of sign changes of Cj. The estimate is reduced by 1 for each relation of the form ∑j=1ncjajr=0.

Bibliographic note

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics