{"paper":{"title":"Bounds for twisted symmetric square $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ritabrata Munshi","submitted_at":"2012-03-04T16:49:16Z","abstract_excerpt":"Let $f\\in S_k(N,\\psi)$ be a newform, and let $\\chi$ be a primitive character of conductor $q^{\\ell}$. Assume that $q$ is a prime and $\\ell>1$. In this paper we describe a method to establish convexity breaking bounds of the form $$ L(\\tfrac{1}{2},\\Sym f\\otimes\\chi)\\ll_{f,\\varepsilon} q^{3/4\\ell-\\delta_{\\ell}+\\varepsilon} $$ for some $\\delta_{\\ell}>0$ and any $\\varepsilon>0$. In particular, for $\\ell=3$ we show that the bound holds with $\\delta_{\\ell}=1/4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0749","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"}