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

Abstract

We prove asymptotics for the density of everywhere locally soluble diagonal quadric surfaces parameterised by rational points on the split quadric surface $y_0{y}_1=y_2{y}_3$ which do not satisfy $-y_0{y}_1=\square$ nor $-y_0{y}_3=\square$.

arXiv commentComments 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