{"paper":{"title":"On the parity of coefficients of eta powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Anna Medvedovsky, Lukas Mauth, Steven Charlton","submitted_at":"2024-11-26T17:55:57Z","abstract_excerpt":"We consider a special subsequence of the Fourier coefficients of powers of the Dedekind $\\eta$-function, analogous to the sequence $\\delta_\\ell := 24^{-1} \\pmod{\\ell}$ on which exceptional congruences of the partition function are supported. Therefrom we define a notion of density $D(r)$ for a normalized eta-power $\\eta^r$ measuring the proportion of primes $\\ell$ for which the order at infinity of $U_\\ell (\\eta^r)$ modulo 2 is maximal. We relate $D(r)$ to a notion of density measuring nonzero prime Fourier coefficients introduced by Bella\\\"iche, and use this to completely classify the vanishi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17638","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.17638/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}