Zhang, Wenpeng; Han, Di On the sixth power mean of the two-term exponential sums. (English) Zbl 1360.11084 J. Number Theory 136, 403-413 (2014). Summary: The main purpose of this paper is using a new analytic method and the properties of Gauss sums to study the computational problem of one kind sixth power mean of two-term exponential sums, and give an interesting identity for it. Cited in 1 ReviewCited in 24 Documents MSC: 11L03 Trigonometric and exponential sums (general theory) 11L05 Gauss and Kloosterman sums; generalizations Keywords:two-term exponential sums; sixth power mean; Gauss sums; identity PDF BibTeX XML Cite \textit{W. Zhang} and \textit{D. Han}, J. Number Theory 136, 403--413 (2014; Zbl 1360.11084) Full Text: DOI References: [1] Apostol, Tom M., Introduction to Analytic Number Theory (1976), Springer-Verlag: Springer-Verlag New York · Zbl 0335.10001 [2] Apostol, Tom M., An extension of the Lehmersʼ picturesque exponential sums, Math. Comp., 61, 203, 25-28 (1993) · Zbl 0781.11031 [3] Berndt, Bruce C., On Gaussian sums and other exponential sums with periodic coefficients, Duke Math. J., 40, 145-156 (1973) · Zbl 0255.10042 [4] Cochrane, T.; Zheng, Z., Bounds for certain exponential sums, Asian J. Math., 4, 757-774 (2000) · Zbl 1030.11040 [5] Cochrane, T.; Pinner, C., Using Stepanovʼs method for exponential sums involving rational functions, J. Number Theory, 116, 270-292 (2006) · Zbl 1093.11058 [6] Cochrane, T.; Zheng, Z., Upper bounds on a two-term exponential sums, Sci. China Ser. A, 44, 1003-1015 (2001) · Zbl 1012.11078 [7] Cochrane, T.; Pinner, C., A further refinement of Mordellʼs bound on exponential sums, Acta Arith., 116, 35-41 (2005) · Zbl 1082.11050 [8] Evans, John W.; Gragg, William B.; LeVeque, Randall J., On least squares exponential sum approximation with positive coefficients, Math. Comp., 34, 149, 203-211 (1980) · Zbl 0424.65002 [9] Hua, L. K., Introduction to Number Theory (1957), Science Press: Science Press Beijing, (Chinese) [10] Weil, A., On some exponential sums, Proc. Natl. Acad. Sci. USA, 34, 204-207 (1948) · Zbl 0032.26102 [11] Williams, Kenneth S., Exponential sums over GF(2n), Pacific J. Math., 40, 511-519 (1972) · Zbl 0241.10024 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.