2016/09/21 by Justin DeBenedetto, Jeremy Rouse, DeBenedetto, Justin +1
Mathematics · #11E20 (Primary) #11F30 (Secondary) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1609.06563
openalex publication_date 2016/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Following Bhargava and Hanke's celebrated 290-theorem, we prove a universality theorem for all positive-definite integer-valued quadratic forms that represent all positive integers coprime to 3. In particular, if a positive-definite quadratic form represents all positive integers coprime to 3 and ≤ 290, then it represents all positive integers coprime to 3. We use similar methods to those used by Rouse to prove (assuming GRH) that a positive-definite quadratic form representing every odd integer between 1 and 451 represents all positive odd integers.