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Inf. Appl."],"accepted":{"date-parts":[[2025,12,31]]},"published-print":{"date-parts":[[2026]]},"abstract":"<jats:p>\n                    This paper establishes explicit evaluations of the 2\n                    <jats:italic>k<\/jats:italic>\n                    -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.\n                  <\/jats:p>","DOI":"10.1051\/ita\/2026001","type":"journal-article","created":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T08:57:57Z","timestamp":1772009877000},"page":"5","source":"Crossref","is-referenced-by-count":0,"title":["2\n                    <i>k<\/i>\n                    -th power mean value of the generalized cubic Gauss sums"],"prefix":"10.1051","volume":"60","author":[{"given":"Ying","family":"Wei","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shaanxi Normal University","place":["PR China"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0375-9691","authenticated-orcid":false,"given":"Tianping","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shaanxi Normal University","place":["PR China"]},{"name":"Research Center for Number Theory and Its Applications, Northwest University","place":["PR China"]}]}],"member":"250","published-online":{"date-parts":[[2026,2,25]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1073\/pnas.34.5.204","volume":"34","author":"Weil","year":"1948","journal-title":"Proc. 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