Northcott property and universality of higher degree forms

2024/07/29 by Om Prakash, Prakash, Om
Business, Management and Accounting · #11E10 #11E76 #11G50 #11H06 #11P05 #11R04 #11R20 #11R80 #FOS: Mathematics #Number Theory (math.NT) #Taxation and Legal Issues

paper · pdf · doi:10.48550/arxiv.2407.19974

openalex publication_date 2024/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a totally real number field, d a positive integer, and Q a higher degree form over K. We prove that there are at most finitely many totally real extensions L/K of degree d such that Q over L is universal. Further, we show that there are no universal forms over totally real infinite extensions of ℚ having the Northcott property.

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