AN ASYMPTOTIC FORMULA FOR REPRESENTATIONS OF INTEGERS BY INDEFINITE HERMITIAN FORMS

作者：Lauret Emilio A^*

来源：Proceedings of the American Mathematical Society, 2014, 142(1): 1-14.

• Representation by hermitian forms
• hyperbolic lattice point theorem

We fix a maximal order O in F = R, C or H, and an F-hermitian form Q of signature (n, 1) with coefficients in O. Let k is an element of N. By applying a lattice point theorem on an n-dimensional F-hyperbolic space, we give an asymptotic formula with an error term, as t -> +infinity, for the number N-t(Q, -k) of integral solutions x is an element of On+1 of the equation Q[x] = - k satisfying vertical bar x(n+1)vertical bar <= t.

• 出版日期2014-1