Open AccessSome identities involving Gauss sums
Author(s) -
Xi Liu
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022180
Subject(s) - gauss sum , gauss , modulo , mathematics , character (mathematics) , prime (order theory) , quadratic gauss sum , order (exchange) , pure mathematics , algebra over a field , arithmetic , combinatorics , physics , geometry , quantum mechanics , finance , economics
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.