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Algebraic degrees of a class of exponential sums. (Chinese. English summary) Zbl 1474.11196

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
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