A new iterative method in Waring's problem
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Publication:1115906
DOI10.1007/BF02392834zbMath0665.10033OpenAlexW2092182987WikidataQ106136058 ScholiaQ106136058MaRDI QIDQ1115906
Publication date: 1989
Published in: Acta Mathematica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02392834
Waring's problem and variants (11P05) Applications of the Hardy-Littlewood method (11P55) Estimates on character sums (11L40) Sieves (11N35)
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Cites Work
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- On sums of positive integral \(k^{th}\) powers
- On Waring's Problem for Smaller Exponents
- On Waring's Problem for Sixth Powers
- On Waring's problem for smaller exponents. II
- An improved upper bound for G(k) in Waring's problem for relatively small k
- Some new estimates for G(k) in Waring's problem
- Homogeneous additive equations and Waring's problem
- On Waring's problem
- Sums of Three Cubes
- Homogeneous additive equations
- A Proof of the Seven Cube Theorem
- On Sums of Positive Integral k-TH Powers
- On Waring's problem for cubes.
- On Waring's problem
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