{"paper":{"title":"Oscillations of coefficients of Dirichlet series attached to automorphic forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jaban Meher, M. Ram Murty","submitted_at":"2014-12-30T06:13:19Z","abstract_excerpt":"For $m\\ge 2$, let $\\pi$ be an irreducible cuspidal automorphic representation of $GL_m(\\mathbb{A}_{\\mathbb{Q}})$ with unitary central character. Let $a_\\pi(n)$ be the $n^{th}$ coefficient of the $L$-function attached to $\\pi$. Goldfeld and Sengupta have recently obtained a bound for $\\sum_{n\\le x} a_\\pi(n)$ as $x \\rightarrow \\infty$. For $m\\ge 3$ and $\\pi$ not a symmetric power of a $GL_2(\\mathbb{A}_{\\mathbb{Q}})$-cuspidal automorphic representation with not all finite primes unramified for $\\pi$, their bound is better than all previous bounds. In this paper, we further improve the bound of Go"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8567","kind":"arxiv","version":3},"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"}