{"paper":{"title":"Average values of L-functions in even characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hwanyup Jung, Sunghan Bae","submitted_at":"2017-01-05T22:38:07Z","abstract_excerpt":"Let $k = \\mathbb{F}_{q}(T)$ be the rational function field over a finite field $\\mathbb{F}_{q}$, where $q$ is a power of $2$. In this paper we solve the problem of averaging the quadratic $L$-functions $L(s, \\chi_{u})$ over fundamental discriminants. Any separable quadratic extension $K$ of $k$ is of the form $K = k(x_{u})$, where $x_{u}$ is a zero of $X^2+X+u=0$ for some $u\\in k$. We characterize the family $\\mathcal I$ (resp. $\\mathcal F$, $\\mathcal F'$) of rational functions $u\\in k$ such that any separable quadratic extension $K$ of $k$ in which the infinite prime $\\infty = (1/T)$ of $k$ r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01493","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":""},"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"}