{"paper":{"title":"On slopes of $L$-functions of $\\mathbb{Z}_p$-covers over the projective line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Hui June Zhu, Michiel Kosters","submitted_at":"2017-01-30T18:05:11Z","abstract_excerpt":"Let $\\mathcal{P}: \\cdots \\rightarrow C_2\\rightarrow C_1\\rightarrow {\\mathbb P}^1$ be a $\\mathbb{Z}_p$-cover of the projective line over a finite field of cardinality $q$ and characteristic $p$ which ramifies at exactly one rational point, and is unramified at other points. In this paper, we study the $q$-adic valuations of the reciprocal roots in $\\mathbb{C}_p$ of $L$-functions associated to characters of the Galois group of $\\mathcal{P}$. We show that for all covers $\\mathcal{P}$ such that the genus of $C_n$ is a quadratic polynomial in $p^n$ for $n$ large, the valuations of these reciprocal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08733","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"}