Regular triangular forms of rank exceeding 3

2022/09/27 by Mingyu Kim, Kim, Mingyu
Mathematics · #11E12 #11E20 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Graph theory and applications #Number Theory (math.NT) #Primary 11D09

paper · pdf · doi:10.48550/arxiv.2209.13238

openalex publication_date 2022/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A triangular form is defined to be an integer-valued quadratic polynomial of the form a₁P₃(x₁)+a₂P₃(x₂)+⋯+a_kP₃(x_k) where a_i's are positive integers and P₃(x)=x(x+1)/2. A triangular form is called regular if it represents all positive integers which are locally represented. In this article, we find all regular triangular forms of more than three variables.

Related

• Regular ternary triangular forms
• A classification of regular diagonal quadratic forms
• The rank of new regular quadratic forms
• Diagonal odd-regular ternary quadratic forms
• The representation of integers by positive ternary quadratic polynomials