Abstract
The main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of quartic Gauss sums, and to give some interesting calculating formulae of them.
Highlights
We all know that these sums occupy a very important position in the study of analytic number theory, and many number theory problems are related to them
Theorem 2 If p is a prime with p ≡ 1(mod8), we have the fourth-order linear recursive formula
Proof We only prove the second formula in Lemma 2
Summary
If p is a prime with p ≡ 5(mod8), one has the identity p–1 We use the analytic methods and the properties of the fourth character modulo p to give an interesting fourth-order linear recursive formula for Vk(p).
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