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1.
K. Farahmand 《Journal of Mathematical Analysis and Applications》1997,210(2):724
This paper, for any constantK, provides an exact formula for the average density of the distribution of the complex roots of equation η0 + η1z + η2z2 + ··· + ηn − 1zn − 1 = Kwhere ηj = aj + ibjand {aj}n − 1j = 0and {bj}n − 1j = 0are sequences of independent identically and normally distributed random variables andKis a complex number withKas its real and imaginary parts. The case of real roots of the above equation with real coefficients andK,z Ris well known. Further we obtain the limiting behaviour of this distribution function asntends to infinity. 相似文献
2.
For all integers m3 and all natural numbers a1,a2,…,am−1, let n=R(a1,a2,…,am−1) represent the least integer such that for every 2-coloring of the set {1,2,…,n} there exists a monochromatic solution to
a1x1+a2x2++am−1xm−1=xm.