{"paper":{"title":"Euler's divergent series in arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anne-Maria Ernvall-Hyt\\\"onen, Louna Sepp\\\"al\\\"a, Tapani Matala-aho","submitted_at":"2018-09-11T13:23:57Z","abstract_excerpt":"Let $\\xi$ and $m$ be integers satisfying $\\xi\\ne 0$ and $m\\ge 3$. We show that for any given integers $a$ and $b$, $b \\neq 0$, there are $\\frac{\\varphi(m)}{2}$ reduced residue classes modulo $m$ each containing infinitely many primes $p$ such that $a-bF_p(\\xi) \\ne 0$, where $F_p(\\xi)=\\sum_{n=0}^\\infty n!\\xi^n$ is the $p$-adic evaluation of Euler's factorial series at the point $\\xi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03859","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"}