| Issue |
RAIRO-Theor. Inf. Appl.
Volume 60, 2026
Diophantine Analysis and Related Topics (DART2025Z)
|
|
|---|---|---|
| Article Number | 5 | |
| Number of page(s) | 12 | |
| DOI | https://doi.org/10.1051/ita/2026001 | |
| Published online | 25 February 2026 | |
2k-th power mean value of the generalized cubic Gauss sums
1
School of Mathematics and Statistics, Shaanxi Normal University,
Xi’an,
710119,
Shaanxi,
PR China
2
Research Center for Number Theory and Its Applications, Northwest University,
Xi’an,
710127,
Shaanxi,
PR China
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
5
November
2025
Accepted:
31
December
2025
Abstract
This paper establishes explicit evaluations of the 2k-th power mean for generalized cubic Gauss sums. By exploiting analytic techniques and fundamental properties of classical Gauss sums, we derive closed-form expressions for these means. Furthermore, we develop a computationally efficient framework for analyzing higher-order moments of such sums.
Mathematics Subject Classification: 11L03 / 11L05
Key words: Cubic Gauss sums / 2k-th power mean value / analytic method / closed-form expression
© The authors. Published by EDP Sciences, 2026
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