Discrete paraboloid
= Discrete paraboloid
{title2=$P=\{(v,v\cdot v):v\in\mathbb F_p^{d-1}\}$}
The discrete paraboloid is the graph of the sum-of-squares <quadratic form> in a vector space over a finite field. Its surface measure is normalized counting measure, of total mass one. A <Fourier extension operator> takes a function on this graph to its character sum in the ambient finite vector space. Ambient counting measure and normalized surface measure must be distinguished when defining a restriction constant.