{"paper":{"title":"On Hecke eigenvalues of Siegel modular forms in the Maass space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Biplab Paul, Jyoti Sengupta, Sanoli Gun","submitted_at":"2018-01-16T17:32:44Z","abstract_excerpt":"In this article, we prove an omega-result for the Hecke eigenvalues $\\lambda_F(n)$ of Maass forms $F$ which are Hecke eigenforms in the space of Siegel modular forms of weight $k$, genus two for the Siegel modular group $Sp_2(\\Z)$. In particular, we prove $$ \\lambda_F(n)= \\Omega(n^{k-1}\\text{exp} (c \\frac{\\sqrt{\\log n}}{\\log\\log n})), $$ when $c>0$ is an absolute constant. This improves the earlier result $$ \\lambda_F(n)= \\Omega(n^{k-1} (\\frac{\\sqrt{\\log n}}{\\log\\log n})) $$ of Das and the third author. We also show that for any $n \\ge 3$, one has $$ \\lambda_F(n) \\leq n^{k-1}\\text{exp} \\left(c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05380","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"}