{"paper":{"title":"The first simultaneous sign change and non-vanishing of Hecke eigenvalues of newforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Balesh Kumar, Biplab Paul, Sanoli Gun","submitted_at":"2018-01-31T18:23:34Z","abstract_excerpt":"Let $f$ and $g$ be two distinct newforms which are normalized Hecke eigenforms of weights $k_1, k_2 \\ge 2$ and levels $N_1, N_2 \\ge 1$ respectively. Also let $a_f(n)$ and $a_g(n)$ be the $n$-th Fourier-coefficients of $f$ and $g$ respectively. In this article, we investigate the first sign change of the sequence $\\{a_f(p^{\\alpha})a_g(p^{\\alpha}) \\}_{p^{\\alpha} \\in \\N, \\alpha \\le 2}$, where $p$ is a prime number. We further study the non-vanishing of the sequence $\\{a_f(n)a_g(n) \\}_{n \\in \\N}$ and derive bounds for first non-vanishing term in this sequence. We also show, using ideas of Kowalski"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10590","kind":"arxiv","version":2},"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"}