{"paper":{"title":"Generic Newton polygon for exponential sums in two variables with triangular base","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Rufei Ren","submitted_at":"2017-01-01T15:55:29Z","abstract_excerpt":"Let $p$ be a prime number. Every two-variable polynomial $f(x_1, x_2)$ over a finite field of characteristic $p$ defines an Artin--Schreier--Witt tower of surfaces whose Galois group is isomorphic to $\\mathbb Z_p$. Our goal of this paper is to study the Newton polygon of the $L$-functions associated to a finite character of $\\mathbb{Z}_p$ and a generic polynomial whose convex hull is a fixed triangle $\\Delta$. We denote this polygon by $\\textrm{GNP}(\\Delta)$. We prove a lower bound of $\\textrm{GNP}(\\Delta)$, which we call the improved Hodge polygon $\\textrm{IHP}(\\Delta)$, and we conjecture tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00254","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"}