{"paper":{"title":"An asymptotic formula for representations of integers by indefinite hermitian forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Emilio A. Lauret","submitted_at":"2011-09-30T00:34:58Z","abstract_excerpt":"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 $|x_{n+1}|\\leq t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6697","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}