{"paper":{"title":"Distributions of Iwasawa $\\lambda$-invariants of $\\mathbf{Z}_p$-towers over supersingular isogeny graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Kosuke Mizuno, Ryosuke Murooka, Sohei Tateno, Taiga Adachi","submitted_at":"2026-05-22T03:08:15Z","abstract_excerpt":"A graph-theoretic analogue of Iwasawa theory, initiated by Gonet and Valli\\`eres, has attracted considerable interest in the study of Iwasawa invariants. On the other hand, for a pair of prime numbers $(r,\\ell)$, one obtains a graph, called the supersingular $\\ell$-isogeny graph (SIG), whose adjacency matrix has eigenvalues given by the $\\ell$-th Fourier coefficients of the weight 2 Eisenstein series and newforms of level $r$. In this paper, we fix prime numbers $r$ and $p$, and let $\\ell$ vary over infinitely many primes. We then investigate the distribution of the Iwasawa $\\lambda$-invariant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23184","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/2605.23184/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"}