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Local solubility for a family of quadrics over a split quadric surface

Tim Browning, Julian Lyczak and Roman Sarapin

Vol. 16 (2023), No. 2, 331–342
Abstract

We study the density of everywhere locally soluble diagonal quadric surfaces, parametrised by rational points that lie on a split quadric surface.

Keywords
quadratic form, local solubility, large sieve, Loughran–Smeets conjecture
Mathematical Subject Classification
Primary: 14G05
Secondary: 11N36, 14D10
Milestones
Received: 13 March 2022
Revised: 2 June 2022
Accepted: 2 June 2022
Published: 26 May 2023

Communicated by Steven J. Miller
Authors
Tim Browning
Institute of Science and Technology Austria
Klosterneuburg
Austria
Julian Lyczak
Institute of Science and Technology Austria
Klosterneuburg
Austria
Roman Sarapin
V. N. Karazin Kharkiv National University
Kharkiv
Ukraine