This paper investigates a high-order two-term exponential sum and its mean value problem. The main focus is on studying the calculation problem of the fourth power mean of the high-order two-term exponential sum. This is done by utilizing the number of solutions of congruence equations and analytic methods. Moreover, concise and interesting identities are also provided.

the high-order two-term exponential sums, fourth power mean, elementary method, analytic method, calculating formula.

Received: December 28, 2023; Revised: February 2, 2024; Accepted: February 20, 2024; Published: February 28, 2024

How to cite this article: Li Wang and Xiaoge Liu, A high-order two-term exponential sum and its mean value problem, JP Journal of Algebra, Number Theory and Applications 63(2) (2024), 153-167. http://dx.doi.org/10.17654/0972555524009

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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