The Hasse Principle for systems of diagonal cubic equations

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• Trevor Wooley, Bristol
• Tuesday 05 February 2008, 16:00-17:00
• MR13, CMS.

If you have a question about this talk, please contact Ben Green.

A conventional application of the Hardy-Littlewood (circle) method establishes the Hasse Principle for a system of R diagonal cubic equations in 8R+1 or more variables provided that the coefficient matrix satisfies appropriate rank conditions. Granted the most ambitious conjectures concerning mean values of Weyl sums, the circle method would conditionally deliver such a conclusion with the number of variables reduced to 6R+1. This limit has been attained for R=1 (R. C. Baker, 1986), and for R=2 (Bruedern and the speaker, 2007). In this talk, we will sketch the ideas underlying the latter conclusion, as well as recent progress on the situation for larger R. In addition to circle method gadgetry to excite the aficionado, there will be plenty of accessible discussion for the non-specialist. (Joint work with Joerg Bruedern).

This talk is part of the Discrete Analysis Seminar series.

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