{"paper":{"title":"W\\lowercase{eyl} \\lowercase {bound for $p$-power twist of} $GL(2)$ L-\\lowercase{functions }","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ritabrata Munshi, Saurabh Kumar Singh","submitted_at":"2017-06-13T10:13:31Z","abstract_excerpt":"Let $f$ be a cuspidal eigenform (holomorphic or Maass) on the full modular group $SL(2, \\mathbb{Z})$ . Let $\\chi$ be a primitive character of modulus $P$. We shall prove the following results:\n 1. Suppose $P = p^r$, where $p$ is a prime and $r\\equiv 0 (\\textrm{mod} \\ 3)$. Then we have \\[ L\\left( f \\otimes \\chi, \\frac{1}{2}\\right) \\ll_{f, \\epsilon} P^{1/3 +\\epsilon}, \\] where $\\epsilon > 0$ is any positive real number.\n  2.   Suppose $\\chi$ factorizes as $\\chi= \\chi_1 \\chi_2$, where $ \\chi_i$'s are primitive character modulo $P_i$, where $P_i$ are primes, $P^{1/2 -\\epsilon} \\ll P_i \\ll P^{1/2 +"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03985","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"}