{"paper":{"title":"On double shifted convolution sum of $SL(2, \\mathbb{Z})$ Hecke eigen forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Saurabh Kumar Singh","submitted_at":"2016-08-25T09:37:18Z","abstract_excerpt":"Let $\\lambda_i (n)$ $i= 1, 2, 3$ denote the normalised Fourier coefficients of holomorphic eigenform or Maass cusp form. In this paper we shall consider the sum: \\[ S:= \\frac{1}{H}\\sum_{h\\leq H} V\\left( \\frac{h}{H}\\right)\\sum_{n\\leq N} \\lambda_1 (n) \\lambda_2 (n+h) \\lambda_3 (n+ 2h)W\\left( \\frac{n}{N} \\right), \\] \\noindent where $V$ and $W$ are smooth bump functions, supported on $[1, 2]$. We shall prove a nontrivial upper bound, under the assumption that $H\\geq N^{1/2+ \\epsilon}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07063","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"}