Forms representing forms: The definite case

Abstract

Let $\psi$ and $F$ be positive definite forms with integral coefficients of equal degree. Using the circle method, we establish an asymptotic formula for the number of identical representations of $\psi$ by $F$, provided $\psi$ is everywhere locally representable and the number of variables of $F$ is large enough. In the quadratic case this supersedes a recent result due to Dietmann and Harvey. Another application addresses the number of primitive linear spaces contained in a hypersurface.

Corrected treatment of the singular series

References in corpus (2)

• On the destruction of minimal foliations
• A note on p-adic solubility for forms in many variables