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Simultaneous Additi...
Simultaneous Additive Equations: Repeated and Differing Degrees
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- Brandes, Julia, 1986 (författare)
- Chalmers tekniska högskola,Chalmers University of Technology,Göteborgs universitet,University of Gothenburg
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- Parsell, S. T. (författare)
- West Chester University
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(creator_code:org_t)
- 2017
- 2017
- Engelska.
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Ingår i: Canadian Journal of Mathematics. - 1496-4279 .- 0008-414X. ; 69:2, s. 258-283
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Abstract
Ämnesord
Stäng
- We obtain bounds for the number of variables required to establish Hasse principles, both for the existence of solutions and for asymptotic formula, for systems of additive equations containing forms of differing degree but also multiple forms of like degree. Apart from the very general estimates of Schmidt and Browning-Heath-Brown, which give weak results when specialized to the diagonal situation, this is the first result on such "hybrid" systems. We also obtain specialized results for systems of quadratic and cubic forms, where we are able to take advantage of some of the stronger methods available in that setting. In particular, we achieve essentially square root cancellation for systems consisting of one cubic and r quadratic equations.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- applications of the Hardy-Littlewood method
- equations in many variables
- counting solutions of Diophantine equations
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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