Asymptotics For Local Solubility Of Diagonal Quadrics Over A Split Quadric Surface

Cameron Wilson

Asymptotics For Local Solubility Of Diagonal Quadrics Over A Split Quadric Surface

Number Theory 2025-07-01 v3

Authors: Cameron Wilson

Abstract

We prove asymptotics for the density of everywhere locally soluble diagonal quadric surfaces parameterised by rational points on the split quadric surface $y_0y_1=y_2y_3$ which do not satisfy $-y_0y_1=\square$ nor $-y_0y_3=\square$ .

Keywords

asymptotic analysis cubic fourfolds

Cite

@article{arxiv.2404.11489,
  title  = {Asymptotics For Local Solubility Of Diagonal Quadrics Over A Split Quadric Surface},
  author = {Cameron Wilson},
  journal= {arXiv preprint arXiv:2404.11489},
  year   = {2025}
}

Comments

Comments welcome. The sections on the neutraliser large sieve and character sum estimates have been moved to a separate paper. Some MAGMA code is now provided to replace some calculations from the final section

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