AN IDENTITY ON THE 2m-TH POWER MEAN VALUE OF THE GENERALIZED GAUSS SUMS
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In this paper, using analytic method and the properties of the Legendre's symbol, we prove an exact calculating formula on the $2m$-th power mean value of the generalized quadratic Gauss sums for $m{\geq}2$. This solves a conjecture of He and Zhang [On the 2k-th power mean value of the generalized quadratic Gauss sums, Bull. Korean Math. Soc. 48 (2011), no. 1, 9-15].
Abstract
In this paper, using analytic method and the properties of the Legendre's symbol, we prove an exact calculating formula on the $2m$-th power mean value of the generalized quadratic Gauss sums for $m{\geq}2$. This solves a conjecture of He and Zhang [On the 2k-th power mean value of the generalized quadratic Gauss sums, Bull. Korean Math. Soc. 48 (2011), no. 1, 9-15].
참고문헌 (6)
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- A. Weil, "On some exponential sums", Proc. Nat. Acad. Sci. U.S.A, 34, pp.204~207 (1948)
- W. P. Zhang, "Moments of generalized quadratic Gauss sums weighted by L-functions", J. Number Theory, 92(2), pp.304~314 (2002)
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