On a question of Davenport and diagonal cubic forms over $$\mathbb{F}_q(t)$$

Leonhard Hochfilzer (University of Göttingen)

Wednesday 28th September, 2022 16:00-17:00 Maths 311B


Does the Hasse principle hold for diagonal cubic forms over $$\mathbb{F}_q(t)$$? Motivated by this question we will study the number of rational solutions of bounded height of diagonal cubic forms in 4 and 6 variables. After giving a brief overview of the history of the Hasse principle for cubics I will sketch how the circle method can be used to tackle and improve this problem. Finally, I will talk about how our results can be used to improve Waring's problem in this context. The talk is based on joint work with Jakob Glas.

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