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The main purpose of this paper is, using the properties of Gauss sums and the estimate for the generalized exponential sums, to study the upper bound estimate problem of one kind sums analogous to the high-dimensional Kloosterman sums and to give some interesting mean value formula and an upper bound estimate for it. MSC: 11L05. © 2013 Li and Han; licensee Springer.

A sum analogous to the high-dimensional Kloosterman sums and its upper bound estimate