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- W1043160959 abstract "Let Fq denote the finite field of odd characteristic p with q elements (q=pe, e∈N) and Fq⁎ represent the nonzero elements of Fq. In this paper, by using the Smith normal form of the index matrix, we give a formula for the number of rational points of the following family of hypersurface over Fq:∑j=0t−1∑i=1rj+1−rjarj+ix1erj+i,1…xnj+1erj+i,nj+1−b=0, where the integers t>0, r0=0<r1<r2<…<rt, n1<n2<…<nt, b∈Fq, ai∈Fq⁎ (i=1,…,rt), and the index of each variable is a positive integer. Especially under some certain conditions, we get an explicit formula of the number of rational points of the above hypersurface. This generalizes greatly the results obtained by Wolfmann in 1994, Sun in 1997 and Wang and Sun in 2005, respectively." @default.
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- W1043160959 date "2015-11-01" @default.
- W1043160959 modified "2023-09-23" @default.
- W1043160959 title "The number of rational points of a family of hypersurfaces over finite fields" @default.
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- W1043160959 doi "https://doi.org/10.1016/j.jnt.2015.04.006" @default.
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