Abstract: | Let Q
1,…,Q
r
be quadratic forms with real coefficients. We prove that the set
is dense in
, provided that the system Q
1(x) = 0,…,Q
r
(x) = 0 has a nonsingular real solution and all forms in the real pencil generated by Q
1,…,Q
r
are irrational and have rank larger than 8r. Moreover, we give a quantitative version of the above assertion. As an application we study higher correlation functions
of the value distribution of a positive definite irrational quadratic form.
Author’s address: Institut für Statistik, Technische Universit?t Graz, A-8010 Graz, Austria |