2017
DOI: 10.1142/s1005386717000475
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The Number of Rational Points of a Family of Algebraic Varieties over Finite Fields

Abstract: Let F q stand for the finite field of odd characteristic p with q elements (q = p n , n ∈ N) and F * q denote the set of all the nonzero elements of F q . Let m and t be positive integers. In this paper, by using the Smith normal form of the exponent matrix, we obtain a formula for the number of rational points on the variety defined by the following system of equations over F q :where the integers t > 0, r 0 = 0 < r 1 < r 2 < ... < r t , 1 ≤ n 1 < n 2 < ... < n t , 0 ≤ j ≤ t − 1, b k ∈ F q , a k,i ∈ F * q , (… Show more

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Cited by 10 publications
(3 citation statements)
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“…Meanwhile, they proposed an interesting question which was recently answerd by Hu and Hong [15]. A more general question was suggested by Hu, Hong and Zhao in [16] that can be stated as follows.…”
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confidence: 99%
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“…Meanwhile, they proposed an interesting question which was recently answerd by Hu and Hong [15]. A more general question was suggested by Hu, Hong and Zhao in [16] that can be stated as follows.…”
mentioning
confidence: 99%
“…But it is kept open when m ≥ 2. Clearly, Yang [36], Song and Chen [25] and Hu and Hong [15] gave a partial answer to Problem 1.1 when m ≥ 2.…”
mentioning
confidence: 99%
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