{"paper":{"title":"Character sums of composite moduli and hybrid subconvexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ritabrata Munshi, Roman Holowinsky, Zhi Qi","submitted_at":"2014-09-12T17:18:34Z","abstract_excerpt":"Let $M=M_1 M_2 M_3$ be the product of three distinct primes and let $\\chi=\\chi_1 \\chi_2 \\chi_3$ be a Dirichlet character of modulus $M$ such that each $\\chi_i$ is a primitive character modulo $M_i$ for $i=1,2,3$. In this paper, we provide a $\\delta$-symbol method for obtaining non-trivial cancellation in smooth character sums of the form $\\sum_{n=1}^\\infty \\chi(n) W(n/N)$, with $N$ roughly of size $\\sqrt M$ and $W$ a smooth compactly supported weight function on $(0, \\infty)$. As a corollary, we establish hybrid subconvexity bounds for the associated Dirichlet $L$-function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3797","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"}