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Simultaneous Additive Equations: Repeated and Differing Degrees

Julia Brandes (Institutionen för matematiska vetenskaper, Algebra och geometri) ; S. T. Parsell
Canadian Journal of Mathematics-Journal Canadien De Mathematiques (0008-414X). Vol. 69 (2017), 2, p. 258-283.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: equations in many variables, counting solutions of Diophantine equations, applications of the Hardy-Littlewood method



Denna post skapades 2017-05-08. Senast ändrad 2017-07-03.
CPL Pubid: 249165

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Algebra och geometriInstitutionen för matematiska vetenskaper, Algebra och geometri (GU)

Ämnesområden

Matematik

Chalmers infrastruktur