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- W4313580554 abstract "<abstract><p>Let $ p $ be a prime, $ k $ be a positive integer, $ q = p^k $, and $ mathbb{F}_q $ be the finite field with $ q $ elements. Let $ mathbb{F}_q^* $ be the multiplicative group of $ mathbb{F}_{q} $, that is $ mathbb{F}_q^* = mathbb{F}_{q}setminus{0} $. In this paper, explicit formulae for the numbers of solutions of cubic diagonal equations $ a_1x_1^3+a_2x_2^3 = c $ and $ b_1x_1^3+b_2x_2^3+b_3x_3^3 = c $ over $ mathbb{F}_q $ are given, with $ a_i, b_jinmathbb{F}_q^* $ $ (1leq ileq 2, 1leq jleq 3) $, $ cinmathbb{F}_q $ and $ pequiv1(rm{mod} 3) $. Furthermore, by using the reduction formula for Jacobi sums, the number of solutions of the cubic diagonal equations $ a_1x_1^3+a_2x_2^3+cdots+a_sx_s^3 = c $ of $ sgeq 4 $ variables with $ a_iinmathbb{F}_q^* $ $ (1leq ileq s) $, $ cinmathbb{F}_q $ and $ pequiv1(rm{mod} 3) $, can also be deduced.</p></abstract>" @default.
- W4313580554 created "2023-01-06" @default.
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- W4313580554 date "2023-01-01" @default.
- W4313580554 modified "2023-10-18" @default.
- W4313580554 title "The number of solutions of cubic diagonal equations over finite fields" @default.
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- W4313580554 doi "https://doi.org/10.3934/math.2023322" @default.
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