{"paper":{"title":"High moments of the Estermann function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sandro Bettin","submitted_at":"2017-01-23T19:40:35Z","abstract_excerpt":"For $a/q\\in\\mathbb{Q}$ the Estermann function is defined as $D(s,a/q):=\\sum_{n\\geq1}d(n)n^{-s}\\operatorname{e}(n\\frac aq)$ if $\\Re(s)>1$ and by meromorphic continuation otherwise. For $q$ prime, we compute the moments of $D(s,a/q)$ at the central point $s=1/2$, when averaging over $1\\leq a<q$.\n  As a consequence we deduce the asymptotic for the iterated moment of Dirichlet $L$-functions $\\sum_{\\chi_1,\\dots,\\chi_k\\mod q}|L(\\frac12,\\chi_1)|^2\\cdots |L(\\frac12,\\chi_k)|^2|L(\\frac12,\\chi_1\\cdots \\chi_k)|^2$, obtaining a power saving error term.\n  Also, we compute the moments of certain functions de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06601","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"}