{"paper":{"title":"On the Fourth Power Moment of the Error Term for the Divisor Problem with Congruence Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jinjiang Li, Min Zhang","submitted_at":"2017-11-29T12:19:00Z","abstract_excerpt":"Let $d(n;\\ell_1,M_1,\\ell_2,M_2)$ denote the number of factorizations $n=n_1n_2$, where each of the factors $n_i\\in\\mathbb{N}$ belongs to a prescribed congruence class $\\ell_i\\bmod M_i\\,(i=1,2)$. Let $\\Delta(x;\\ell_1,M_1,\\ell_2,M_2)$ be the error term of the asymptotic formula of $\\sum\\limits_{n\\leqslant x}d(n;\\ell_1,M_1,\\ell_2,M_2)$. In this paper, we establish an asymptotic formula of the fourth power moment of $\\Delta(M_1M_2x;\\ell_1,M_1,\\ell_2,M_2)$ and prove that \\begin{equation*}\n  \\int_1^T\\Delta^4(M_1M_2x;\\ell_1,M_1,\\ell_2,M_2)\\mathrm{d}x=\\frac{1}{32\\pi^4}C_4\\Big(\\frac{\\ell_1}{M_1},\\frac{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10808","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"}