Let p be an odd prime with p ≡ 1 mod 4, k be any positive integer, ψ be any fourth-order character mod p. In this paper, we use the analytic method and the properties of character sums mod p to study the computational problem of G(k, p) = τk(ψ)+τk(ψ), and give an interesting fourth-order linear recurrence formula for it, where τ(ψ) denotes the classical Gauss sums.
@article{bwmeta1.element.doi-10_1515_math-2017-0104,
author = {Chen Zhuoyu and Zhang Wenpeng},
title = {On the fourth-order linear recurrence formula related to classical Gauss sums},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {1251-1255},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0104}
}
Chen Zhuoyu; Zhang Wenpeng. On the fourth-order linear recurrence formula related to classical Gauss sums. Open Mathematics, Tome 15 (2017) pp. 1251-1255. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0104/