### 100% Hasse principle for Châtelet surfaces

Heilbronn Number Theory Seminar

18th October 2023, 4:00 pm – 5:00 pm

Fry Building, 2.04

In a joint work with Skorobogatov [arXiv:2005.02998] we proved Schinzel's Hypothesis in 100% of the cases and as an immediate corollary we obtained that a positive proportion of Châtelet surfaces satisfy the Hasse principle. In the talk I will explain subsequent joint work with Tim Browning and Joni Teräväinen [arXiv:2212.10373] that generalises the previous von Mangoldt result to more general arithmetic functions and as a consequence proves the Hasse principle for 100% of Châtelet surfaces.

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