Systems of forms of the same degree

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• Simon Leo Rydin Myerson (University of Oxford)
• Tuesday 03 May 2016, 14:15-15:15
• MR13.

If you have a question about this talk, please contact G. Rosso.

Let f = (f_1,...,f_R) be a system of forms of degree d in n variables. A classic result of Birch estimates the number of integral zeroes of f of bounded height, when n >>_{d,R} 1 is large and the variety f = 0 is smooth. We give an improvement when R >>_d 1 is large, and an extension to systems of Diophantine inequalities | f_i | < 1 with real coefficients. Our strategy reduces the problem to an upper bound for the number of solutions to a multilinear auxiliary inequality, comparable to an auxiliary equation introduced by Dietmann and Schindler.

This talk is part of the Number Theory Seminar series.

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