{"paper":{"title":"Special L-values and Selmer groups of Siegel modular forms of genus 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Xiaoyu Zhang","submitted_at":"2018-11-05T20:55:44Z","abstract_excerpt":"Let $p$ be an odd prime, $N$ a square-free odd positive integer prime to $p$, $\\pi$ a $p$-ordinary cohomological irreducible cuspidal automorphic representation of $\\mathrm{GSp}_4(\\mathbb{A}_\\mathbb{Q})$ of principal level $N$ and Iwahori level at $p$. Using a $p$-integral version of Rallis inner product formula and modularity theorems for $\\mathrm{GSp}_{4/\\mathbb{Q}}$ and $\\mathrm{U}_{4/\\mathbb{Q}}$, we establish an identity between the $p$-part of the critical value at $1$ of the degree $5$ $L$-function of $\\pi$ twisted by the non-trivial quadratic Dirichlet character $\\xi$ associated to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02031","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"}