Cyoclotomic Numbers Of Order 2l² With Prime L

2018/07/20 by Helal Ahmed, Ahmed, Md. Helal, Jagmohan Tanti +3
Mathematics · Physics and Astronomy · #11T22 (Secondary) #11T24 (Primary) #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #F.2.2 #FOS: Mathematics #I.2.7 #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1807.07708

openalex publication_date 2018/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The problem of determining cyclotomic numbers in terms of the solutions of certain Diophantine systems has been treated by many authors since the age of Gauss. In this paper we obtain an explicit expression for cyclotomic numbers of order 2l² in terms of the coefficients of the Jacobi sums of lower orders. At the end, we illustrate the nature of two matrices corresponding to two types of cyclotomic numbers.

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