Representation of large numbers by ternary quadratic forms

E. P. Golubeva

Sbornik. Mathematics, Tome 57 (1987) no. 1, pp. 43-56

Résumé

Assuming a nontrivial displacement of the zeros of Dirichlet $L$-functions with quadratic characters, the author obtains asymptotic formulas for the number of lattice points in regions on the surface $n=f(x,y,z)$ $(n\to\infty)$, where $f(x,y,z)$ is an arbitrary nondegenerate integral quadratic form, $n\ne n_1n_2^2$, and $n_1$ is a divisor of twice the discriminant of $f$. The cases of an ellipsoid, a two-sheeted hyperboloid, and a one-sheeted hyperboloid are examined in a uniform way. Bibliography: 25 titles.