{"paper":{"title":"Shifted Character Sums with Multiplicative Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chaohua Jia, Ke Gong","submitted_at":"2014-04-08T16:45:40Z","abstract_excerpt":"Let $f(n)$ be a multiplicative function satisfying $|f(n)|\\leq 1$, $q$ $(\\leq N^2)$ be a prime number and $a$ be an integer with $(a,\\,q)=1$, $\\chi$ be a non-principal Dirichlet character modulo $q$. In this paper, we shall prove that $$ \\sum_{n\\leq N}f(n)\\chi(n+a)\\ll {N\\over q^{1\\over 4}}\\log\\log(6N)+q^{1\\over 4}N^{1\\over 2}\\log(6N)+{N\\over \\sqrt{\\log\\log(6N)}}. $$\n  We shall also prove that \\begin{align*} &\\sum_{n\\leq N}f(n)\\chi(n+a_1)\\cdots\\chi(n+a_t)\\ll {N\\over q^{1\\over 4}}\\log\\log(6N)\\\\ &\\quad+q^{1\\over 4}N^{1\\over 2}\\log(6N)+{N\\over \\sqrt{\\log\\log(6N)}}, \\end{align*} where $t\\geq 2$, $a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2204","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"}