# AN IDENTITY ON THE 2m-TH POWER MEAN VALUE OF THE GENERALIZED GAUSS SUMS

• Liu, Feng (School of Mathematical Sciences Nanjing Normal University) ;
• Yang, Quan-Hui (School of Mathematical Sciences Nanjing Normal University)
• Received : 2011.06.30
• Published : 2012.11.30

#### 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].

#### Acknowledgement

Supported by : National Natural Science Foundation of China

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