{"paper":{"title":"On the third moment of $L\\big(\\frac{1}{2}, \\chi_{d}\\big)$ I: the rational function field case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adrian Diaconu","submitted_at":"2018-01-01T17:59:50Z","abstract_excerpt":"In this note, we prove the existence of a secondary term in the asymptotic formula of the cubic moment of quadratic Dirichlet L-functions $$\\sum_{\\substack{d - \\mathrm{monic \\, \\& \\, sq. \\, free} \\mathrm{deg}\\, d \\, = \\, D}} L\\big(\\tfrac{1}{2}, \\chi_{d}\\big)^{3}$$ over rational function fields on the order of $q^{\\scriptscriptstyle \\frac{3}{4} D}.$ This term is in perfect analogy with the $x^{\\scriptscriptstyle \\frac{3}{4}}$-term indicated in our joint work arXiv:math/0110092v1 for the corresponding asymptotic formula over the rationals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00486","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"}