{"paper":{"title":"Zeros of certain combinations of Eisenstein series of weight 2k, 3k, and k + l","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jetjaroen Klangwang","submitted_at":"2019-07-09T15:51:57Z","abstract_excerpt":"We locate the zeros of the modular forms $E_k^2(\\tau) + E_{2k}(\\tau), E_k^3(\\tau) + E_{3k} (\\tau),$ and $E_k(\\tau)E_l(\\tau) +E_{k+l}(\\tau),$ where $E_k(\\tau)$ is the Eisenstein series for the full modular group $\\text{SL}_2(\\mathbb{Z})$. By utilizing work of F.K.C. Rankin and Swinnerton-Dyer, we prove that for sufficiently large $k,l$, all zeros in the standard fundamental domain are located on the lower boundary $\\mathcal{A} = \\{ e^{i\\theta} : \\pi/2 \\leq \\theta \\leq 2\\pi/3\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04259","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"}