Cubic Forms and the Circle Method

Tim Browning is a professor of number theory with a focus on analytic number theory and Diophantine geometry. 

- 1. Cubic Forms Over Local Fields. - 2. Waring's Problem for Cubes. - 3. Cubic Forms via Weyl Differencing. - 4. Norm Forms Over Number Fields. - 5. Diagonal Cubic Forms Over Function Fields. - 6. Lines on Cubic Hypersurfaces.

"This marvelous and very clearly written book is a very valuable addition to the literature ... . I think it is a great read for every circle method practitioner, especially those coming from the more classical side but eager to learn more about the function field or geometric side, as well as for graduate students in analytic number theory, to be studied along with the more classical texts by Davenport and Vaughan." (Rainer Dietmann, Mathematical Reviews, March, 2024)

"It is recommended for readers with a solid background in abstract algebra, local fields, algebraic varieties and some analytic and algebraic number theory." (Franz Lemmermeyer, zbMATH 1493.11003, 2022)