2024/09/26 by Mikuláš Zindulka, Zindulka, Mikuláš
Computer Science · Mathematics · #11A55 #11P81 (Secondary) #11R11 (Primary) 11R80 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2409.18080
openalex publication_date 2024/09/26 · openalex created_date 2024/10/27 · openalex updated_date 2026/07/28
In this paper, we study partitions of totally positive integral elements α in a real quadratic field K. We prove that for a fixed integer m ≥ 1, an element with m partition exists in almost all K. We also obtain an upper bound for the norm of α that can be represented as a sum of indecomposables in at most m ways, completely characterize the α's represented in exactly 2 ways, and subsequently apply this result to complete the search for fields containing an element with m partitions for 1 ≤ m ≤ 7.