{"paper":{"title":"Moments of real Dirichlet $L$-functions and multiple Dirichlet series","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Martin \\v{C}ech","submitted_at":"2024-02-12T08:19:10Z","abstract_excerpt":"We consider the multiple Dirichlet series associated to the $k$th moment of real Dirichlet $L$-functions, and prove that it has a meromorphic continuation to a specific region in $\\mathbb{C}^{k+1}$, which is conditional under the generalized Lindel\\\"of hypothesis for $k\\geq 5$.\n  As a corollary, we obtain asymptotic formulas for the first three moments with a power-saving error term, and detect the 0- and 1-swap terms in related problems for any $k$ (conditionally under the Generalized Lindel\\\"of Hypothesis), recovering the recent results of Conrey and Rodgers on long Dirichlet polynomials.\n  "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.07473","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.07473/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}