{"paper":{"title":"Limits of traces of singular moduli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dohoon Choi, Subong Lim","submitted_at":"2018-09-09T08:18:08Z","abstract_excerpt":"Let $f$ and $g$ be weakly holomorphic modular functions on $\\Gamma_0(N)$ with the trivial character. For an integer $d$, let $\\Tr_d(f)$ denote the modular trace of $f$ of index $d$. Let $r$ be a rational number equivalent to $i\\infty$ under the action of $\\Gamma_0(4N)$. In this paper, we prove that, when $z$ goes radially to $r$, the limit $Q_{\\hat{H}(f)}(r)$ of the sum $H(f)(z) = \\sum_{d>0}\\Tr_d(f)e^{2\\pi idz}$ is a special value of a regularized twisted $L$-function defined by $\\Tr_d(f)$ for $d\\leq0$. It is proved that the regularized $L$-function is meromorphic on $\\mathbb{C}$ and satisfies"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02938","kind":"arxiv","version":1},"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"}