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- W2964140537 abstract "In this paper we mainly focus on some determinants with Legendre symbol entries. Let p be an odd prime and let (⋅p) be the Legendre symbol. We show that (−S(d,p)p)=1 for any d∈Z with (dp)=1, and that(Wpp)={(−1)|{0<k<p4:(kp)=−1}|ifp≡1(mod4),(−1)⌊(p+1)/8⌋ifp≡3(mod4), whereS(d,p)=det[(i2+dj2p)]1⩽i,j⩽(p−1)/2 andWp=det[(i2−((p−1)/2)!jp)]0⩽i,j⩽(p−1)/2. We also pose some conjectures on determinants, one of which states that (−1)⌊(p+1)/8⌋Wp is a square when p≡3(mod4)." @default.
- W2964140537 created "2019-07-30" @default.
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- W2964140537 date "2019-03-01" @default.
- W2964140537 modified "2023-10-15" @default.
- W2964140537 title "On some determinants with Legendre symbol entries" @default.
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- W2964140537 doi "https://doi.org/10.1016/j.ffa.2018.12.004" @default.
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