A Universal Quaternary Quadratic Form over Gaussian Integers

2013/10/23 by Felix Sidokhine, Sidokhine, Felix
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1310.6293

openalex publication_date 2013/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we show that the form x² + iy² + z² + iw² represents all gaussian integers. The main tools used in this proof are Fermat's little theorem (over finite field extensions), the Mordell-Niven theorem (representation of some gaussians), and the generalized Euler-identity over finite field extensions.

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