{"paper":{"title":"Non-vanishing of Rankin-Selberg Convolutions for Hilbert Modular Form","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alia Hamieh, Naomi Tanabe","submitted_at":"2018-06-12T20:17:42Z","abstract_excerpt":"In this paper, we study the non-vanishing of the central values of the Rankin-Selberg $L$-function of two ad\\`elic Hilbert primitive forms ${\\bf f}$ and ${\\bf g}$, both of which have varying weight parameter $k$. We prove that, for sufficiently large $k$, there are at least $\\frac{k}{(\\log k)^{c}}$ ad\\`elic Hilbert primitive forms ${\\bf f}$ of weight $k$ for which $L(\\frac12, {\\bf f}\\otimes{\\bf g})$ are nonzero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04749","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"}