Chen, Chao; Peng, Guohua Algebraic degrees of a class of exponential sums. (Chinese. English summary) Zbl 1474.11196 J. Sichuan Univ., Nat. Sci. Ed. 57, No. 6, 1029-1032 (2020). Summary: Recently, the algebraic degrees of the exponential sums \(S_q(f)\) over a finite field \(\mathbb F_q\) were studied. In this article, based on the results above, we discuss the Gaussian sums in the case of \(q = p^2\) and \(p \equiv 1\pmod 4\) and obtain that \(S_q(x^d)\) has only two possible values if it is of degree 1. Additionally, we get all explicit values of the algebraic degrees of Gaussian sums in some special cases. MSC: 11T23 Exponential sums 11T24 Other character sums and Gauss sums Keywords:exponential sum; Gaussian sum; algebraic degree; finite field PDFBibTeX XMLCite \textit{C. Chen} and \textit{G. Peng}, J. Sichuan Univ., Nat. Sci. Ed. 57, No. 6, 1029--1032 (2020; Zbl 1474.11196)