{"paper":{"title":"On the Correlations, Selberg Integral and Symmetry of Sieve Functions in Short Intervals","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Giovanni Coppola","submitted_at":"2007-09-23T16:54:09Z","abstract_excerpt":"We study the arithmetic (real) function f=g*1, with g \"essentially bounded\" and supported over the integers of [1,Q]. In particular, we obtain non-trivial bounds, through f \"correlations\", for the \"Selberg integral\" and the \"symmetry integral\" of f in almost all short intervals [x-h,x+h], N<x<2N, beyond the \"classical\" level, up to level of distribution, say, lambda=log Q/log N < 2/3 (for enough large h). This time we don't apply Large Sieve inequality, as in our paper [C-S]. Precisely, our method is completely elementary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.3648","kind":"arxiv","version":3},"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"}