{"paper":{"title":"Sum of the $GL(3)$ Fourier coefficients over mixed powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Himanshi Chanana, Saurabh Kumar Singh","submitted_at":"2023-10-17T17:15:27Z","abstract_excerpt":"Let $A(n)$ be the $(1,n)$-th Fourier coefficients of $SL(3,\\mathbb{Z})$ Hecke-Maass cusp form, denoted as $A(1,n)$ or the triple divisor function, denoted as $d_3(n)$. Let $k \\geqslant3$ be an integer. In this paper, we establish an asymptotic formula for the sum \\begin{equation*}\n  \\mathop{\\sum}_{\\substack{1 \\leqslant n_1, n_2 \\leqslant X^{1/2} \\\\ 1 \\leqslant n_3 \\leqslant X^{1/k}}} A(Q(n_1,n_2) + n_3^k)\\mathsf{a}(n_3), \\end{equation*} where $\\mathsf{a}(n)$ is either von-Mangoldt function or identity function, and $Q(x,y) \\in \\mathbb{Z}[x,y]$ is a binary quadratic polynomial. When $A(n)=A(1,n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.11408","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.11408/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}