Using Hooley neutralisers, a large sieve for quadratic characters is improved for multiplicatively weighted sequences, with applications to hyperbolic-region character sums.
Asymptotics For Local Solubility Of Diagonal Quadrics Over A Split Quadric Surface
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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 $-y_0y_3=\square$.
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An improved large sieve for quadratic characters via Hooley neutralisers and its applications
Using Hooley neutralisers, a large sieve for quadratic characters is improved for multiplicatively weighted sequences, with applications to hyperbolic-region character sums.