A Conjecture of Zhi-Wei Sun on Determinants Over Finite Fields
نویسندگان
چکیده
In this paper, we study certain determinants over finite fields. Let $\mathbb{F}_q$ be the field of $q$ elements and let $a_1,a_2,\cdots,a_{q-1}$ all nonzero $\mathbb{F}_q$. $T_q=\left[\frac{1}{a_i^2-a_ia_j+a_j^2}\right]_{1\le i,j\le q-1}$ a matrix We obtain explicit value $\det T_q$. Also, as consequence our result, confirm conjecture posed by Zhi-Wei Sun.
منابع مشابه
Notes on Conjectures of Zhi-wei Sun
Conjecture 1 (1988-04-23). Let a0, . . . , an−1, b0, . . . , bn−1 ∈ N. Suppose that ∑n−1 r=0 are 2πir/n = ∑n−1 r=0 bre , and that the least prime divisor p = p(n) of n is greater than |{0 6 r < n : ar 6= 0}| and |{0 6 r < n : br 6= 0}|. Then ar = br for all r ∈ R(n) = {0, 1, . . . , n− 1}. Remark 1. M. Newman [Math. Ann. 1971] showed that if c0, . . . , cn−1 ∈ Q, ∑n−1 r=0 cre 2πir/n = 0 and |{0...
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ژورنال
عنوان ژورنال: Bulletin of the Malaysian Mathematical Sciences Society
سال: 2022
ISSN: ['2180-4206', '0126-6705']
DOI: https://doi.org/10.1007/s40840-022-01357-2