An asymptotic formula for representations of integers by indefinite hermitian forms

Details An asymptotic formula for representations of integers by indefinite hermitian forms An asymptotic formula for representations of integers by indefinite hermitian forms

2011-09-30

arxiv.org/abs/1109.6697v1

Mathematics

Number Theory

Scientific paper

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

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