On Hilbert's solution of Waring's problem (Q539203)
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scientific article; zbMATH DE number 5900633
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Hilbert's solution of Waring's problem |
scientific article; zbMATH DE number 5900633 |
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On Hilbert's solution of Waring's problem (English)
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27 May 2011
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By elementary (no ``circle'' method allowed), albeit clever, methods the author gives an upper bound \(B(k)\) for the minimal number \(g(k)\) of \(k\)-th powers necessary to write any positive integer as as sum of \(g(k)\) \(k\)-th powers of positive integers. Indeed \[ B(k) := k^{(15+o(1))(2k)^{5}}, \] improving on previous results of this kind. Some historical background on the problem is recalled.
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sums of \(k\)-th powers of positive integers
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variant of Waring's problem
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polynomial identities
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elementary methods
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