{"paper":{"title":"Bounds on short character sums and L-functions for characters with a smooth modulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Igor Shparlinski, William Banks","submitted_at":"2016-05-24T17:35:01Z","abstract_excerpt":"We combine a classical idea of Postnikov (1956) with the method of Korobov (1974) for estimating double Weyl sums, deriving new bounds on short character sums when the modulus $q$ has a small core $\\prod_{p\\mid q}p$. Using this estimate, we improve certain bounds of Gallagher (1972) and Iwaniec (1974) for the corresponding $L$-functions. In turn, this allows us to improve the error term in the asymptotic formula for primes in short arithmetic progressions modulo a power of a fixed prime. As yet another application of our bounds, we substantially extend the region free of Siegel zeros."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07553","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"}