{"paper":{"title":"Nonexistence results of generalized bent functions from $\\mathbb{Z}_3^n$ to $ \\mathbb{Z}_m$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Priya Dhankhar, Sanjay Kumar Singh","submitted_at":"2026-05-14T14:38:03Z","abstract_excerpt":"In this paper, we investigate generalized bent functions (GBFs) from $\\mathbb{Z}_3^n$ to $\\mathbb{Z}_m$. We show that GBFs exist whenever $3$ divides $m$, while several nonexistence results are obtained when $3\\nmid m$. In particular, we prove that no GBFs exist for $n=1,2$ when $m$ is odd and not divisible by $3$. For the case $n=3$, we establish the nonexistence of GBFs $f:\\mathbb{Z}_3^3 \\rightarrow \\mathbb{Z}_{5\\cdot11^r}$ for all nonnegative integers $r$. Finally, we show that no GBF exists from $\\mathbb{Z}_3$ to $\\mathbb{Z}_{2m'}$ and $\\mathbb{Z}_3^2$ to $\\mathbb{Z}_{2m'}$, where $m'$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.14895","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"}