SUP[ENF (ω)2/πLn N] 0.6312…AND INF[ENF(ω)-2/πLn N]-The superior limit to the average number of real roots of a random algebraic equation

Wang Youjing

Journal of Nanjing Forestry University (Natural Sciences Edition） ›› 1984, Vol. 8 ›› Issue (03) : 113-118.

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南京林业大学学报（自然科学版）
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Journal of Nanjing Forestry University (Natural Sciences Edition） ›› 1984, Vol. 8 ›› Issue (03) : 113-118. DOI: 10.3969/j.jssn.1000-2006.1984.03.017

SUP[ENF (ω)2/πLn N] 0.6312…AND INF[ENF(ω)-2/πLn N]-The superior limit to the average number of real roots of a random algebraic equation

  • Wang Youjing
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Abstract

In this paper, we proveTheorem Let Fn(ω,t) = be a random algebraic eguation, wherea1(ω) (i=0, 1,2,…,n-1) are independent Gaussian random variables with mean o and standard deviation 1, then for n≥2, we havesup[ENF(ω)-2/π1nn=inf [ENF(ω)-2/π1lnn]=1-2/π1n2≈0.558728…

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Wang Youjing. SUP[ENF (ω)2/πLn N] 0.6312…AND INF[ENF(ω)-2/πLn N]-The superior limit to the average number of real roots of a random algebraic equation[J]. Journal of Nanjing Forestry University (Natural Sciences Edition）. 1984, 8(03): 113-118 https://doi.org/10.3969/j.jssn.1000-2006.1984.03.017
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