{"paper":{"title":"On properties of the Taylor series coefficients of the Riemann xi function at $s=\\frac{1}{2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Mario DeFranco","submitted_at":"2019-07-21T14:40:56Z","abstract_excerpt":"We prove some properties about the non-zero Taylor series coefficients $a_k$ of the Riemann xi function $\\xi(s)$ at $s=\\frac{1}{2}$. In particular, we present integral formulas that evaluate $a_k$ whose integrands involve a Gaussian function and a function we call $L(x;k)$. We use these formulas to show that $a_k$ is positive. We also define a sequence of polynomials $p(x;n)$ which arise naturally from the integral formulas and use them to prove that the coefficients $a_k$ are decreasing."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08984","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"}