Some identities involving Gauss sums

Xi Liu; Xi Liu

doi:10.3934/math.2022180

AIMS Mathematics

2022, Volume 7, Issue 2: 3250-3257. doi: 10.3934/math.2022180

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Some identities involving Gauss sums

Xi Liu ^,

School of Mathematics, Northwest University, Xi'an, Shaanxi, China

Received: 15 July 2021 Accepted: 18 November 2021 Published: 29 November 2021
MSC : 11L10, 11L40

We calculate several identities involving some Gauss sums of the $ 2^k $-order character modulo an odd prime $ p $ by using the elementary and analytic methods, and finally give several exact and interesting formulae for them. The properties of the classical Gauss sums play an important role in the proof of this paper.
- $ 2^k $-order character,
- the classical Gauss sums,
- analytic methods,
- identity,
- calculating formula
Citation: Xi Liu. Some identities involving Gauss sums[J]. AIMS Mathematics, 2022, 7(2): 3250-3257. doi: 10.3934/math.2022180

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Abstract

We calculate several identities involving some Gauss sums of the $ 2^k $-order character modulo an odd prime $ p $ by using the elementary and analytic methods, and finally give several exact and interesting formulae for them. The properties of the classical Gauss sums play an important role in the proof of this paper.

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