{"paper":{"title":"The (S,{2})-Iwasawa theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Min-Soo Kim, Su Hu","submitted_at":"2013-10-16T03:43:01Z","abstract_excerpt":"Iwasawa made the fundamental discovery that there is a close connection between the ideal class groups of $\\mathbb{Z}_{p}$-extensions of cyclotomic fields and the $p$-adic analogue of Riemann's zeta functions $$\\zeta(s)=\\sum_{n=1}^{\\infty}\\frac{1}{n^{s}}.$$\n  In this paper, we show that there may also exist a parallel Iwasawa's theory corresponding to the $p$-adic analogue of Euler's deformation of zeta functions $$\\phi(s)=\\sum_{n=1}^{\\infty}\\frac{(-1)^{n-1}}{n^{s}}.$$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4257","kind":"arxiv","version":5},"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"}