{"paper":{"title":"The $p$-Adic Valuations of Weil Sums of Binomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Daniel J. Katz, Philippe Langevin, Sangman Lee, Yakov Sapozhnikov","submitted_at":"2016-08-14T01:52:26Z","abstract_excerpt":"We investigate the $p$-adic valuation of Weil sums of the form $W_{F,d}(a)=\\sum_{x \\in F} \\psi(x^d -a x)$, where $F$ is a finite field of characteristic $p$, $\\psi$ is the canonical additive character of $F$, the exponent $d$ is relatively prime to $|F^\\times|$, and $a$ is an element of $F$. Such sums often arise in arithmetical calculations and also have applications in information theory. For each $F$ and $d$ one would like to know $V_{F,d}$, the minimum $p$-adic valuation of $W_{F,d}(a)$ as $a$ runs through the elements of $F$. We exclude exponents $d$ that are congruent to a power of $p$ m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04047","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"}