{"paper":{"title":"Sub-convexity problem for Rankin-Selberg $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chandrasekhar Raju","submitted_at":"2018-07-29T18:08:08Z","abstract_excerpt":"We establish a sub-convexity estimate for Rankin-Selberg $L$-functions in the combined level aspect, using the circle method. If $p$ and $q$ are distinct prime numbers, $f$ and $g$ are non-exceptional newforms (modular or Maass) for the congruence subgroups $\\Gamma_0(p)$ and $\\Gamma_0(q)$ (resp) with trivial nebentypus, then for all $\\epsilon >0$ we show that there exists an $A >0$ such that $$ L\\left(\\frac{1}{2}+it, f \\times g \\right) \\ll_{\\epsilon,\\mu_f, \\mu_g}(1+|t|)^A \\frac{(pq)^{1/2+\\epsilon}}{\\max\\{p,q \\}^{\\frac{1}{64}}}. $$ The dependence on $\\mu_f$ and $\\mu_g$, the parameters at infini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11092","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"}