{"paper":{"title":"Asymptotic formulas for sums of elements from a multiplicative group","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Florian Luca, Jan-Hendrik Evertse, K\\'alm\\'an Gy\\H{o}ry, Lajos Hajdu, L\\'aszl\\'o Remete","submitted_at":"2026-05-27T18:22:59Z","abstract_excerpt":"Let $K$ be a number field, $k\\geq 2$ an integer, $(K^*)^k$ the $k$-fold direct product of $K^*$ with coordinatewise multiplication, and $\\Gamma$ a finitely generated subgroup of rank $r$ of $(K^*)^k$. Further, let $H(\\alpha )$ denote the absolute exponential height of an algebraic number $\\alpha$. Fix non-zero elements $a_1\\kdots a_k\\in K$. We give asymptotic formulas for the number of $\\mathbf{x}=(x_1\\kdots x_k)\\in\\Gamma$ with $H(a_1x_1+\\cdots +a_kx_k)\\leq X$ as $X\\to\\infty$ such that no non-empty subsum of $a_1x_1+\\cdots +a_kx_k$ vanishes. By the same method of proof, we obtain an asymptotic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28973","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/2605.28973/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"}