An asymptotic formula for representations of integers by indefinite hermitian forms

LAURET, EMILIO

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

AMER MATHEMATICAL SOC

Lugar: Providence, USA; Año: 2012

0002-9939

We fix a maximal order $mathcal O$ in $mathbb{F}=mathbb{R},mathbb{C}$ or $mathbb{H}$, and an $mathbb{F}$-hermitian form $Q$ of signature $(n,1)$ with coefficients in $mathcal O$. Let $kinmathbb{N}$. By applying a lattice point theorem on $n$-dimensional $mathbb{F}$-hyperbolic space, we give an asymptotic formula with an error term, as $t o+infty$, for the number $N_t(Q,-k)$ of integral solutions $xinmathcal O^{n+1}$ of the equation $Q[x]=-k$ satisfying $|x_{n+1}|leq t$.