{"paper":{"title":"On the Fourth Power Moment of Fourier Coefficients of Cusp Form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jinjiang Li, Min Zhang, Panwang Wang","submitted_at":"2017-02-01T08:43:04Z","abstract_excerpt":"Let $a(n)$ be the Fourier coefficients of a holomorphic cusp form of weight $\\kappa=2n\\geqslant12$ for the full modular group and $A(x)=\\sum\\limits_{n\\leqslant x}a(n)$. In this paper, we establish an asymptotic formula of the fourth power moment of $A(x)$ and prove that \\begin{equation*}\n  \\int_1^TA^4(x)\\mathrm{d}x=\\frac{3}{64\\kappa\\pi^4}s_{4;2}(\\tilde{a}) T^{2\\kappa}+O\\big(T^{2\\kappa-\\delta_4+\\varepsilon}\\big) \\end{equation*} with $\\delta_4=1/8$, which improves the previous result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00163","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"}