On the classical Gauss sum and the recursive properties

• Published in: Advances in difference equations Vol. 2018; no. 1; pp. 1 - 6
• Main Authors: Bai, Hui, Hu, Jiayuan
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 23.10.2018; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Analytic method; Difference and Functional Equations; Eighth character; Functional Analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Polynomials; Rational polynomial; Second-order linear recursive formula; The classical Gauss sum; Rational polynomial; Analytic method; 11L05; The classical Gauss sum; Eighth character; Second-order linear recursive formula
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-018-1804-7

Let p be a prime with p ≡ 1 mod 8 , ψ be an eighth character mod p , and τ ( ψ ) denote the classical Gauss sum mod p . The main purpose of this paper is using the analytic method and the properties of the classical Gauss sum to study the computational problem of one kind rational polynomial of τ ( ψ ) . In the end, we prove an interesting second-order linear recursive formula for it.