{"paper":{"title":"On the Rankin-Selberg problem in short intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivi\\'c","submitted_at":"2011-09-07T08:12:00Z","abstract_excerpt":"If $$ \\Delta(x) \\;:=\\; \\sum_{n\\leqslant x}c_n - Cx\\qquad(C>0) $$ denotes the error term in the classical Rankin-Selberg problem, then we obtain a non-trivial upper bound for the mean square of $\\Delta(x+U) - \\Delta(x)$ for a certain range of $U = U(X)$. In particular, under the Lindel\\\"of hypothesis for $\\zeta(s)$, it is shown that $$ \\int_X^{2X} \\Bigl(\\Delta(x+U)-\\Delta(x)\\Bigr)^2\\,{\\roman d} x \\;\\ll_\\epsilon\\; X^{9/7+\\epsilon}U^{8/7}, $$ while under the Lindel\\\"of hypothesis for the Rankin-Selberg zeta-function the integral is bounded by $X^{1+\\epsilon}U^{4/3}$. An analogous result for the d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1385","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"}