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On the Distribution of Roots of Polynomials
The Annals of Mathematics, 1950Soit \(f(z)=a_0+a_1z+ \cdots + a_nz^n\) un polynôme de degré \(n\) à coefficients complexes, et posons \(P={|a_o|+ \cdots +|a_n| \over \sqrt {|a_0 a_n|}}\). Soient \(z_\nu =r_\nu e^{i\varphi_\nu} (1 \leq \nu \leq n)\) les racines de ce polynôme; les AA., par un ingénieux raisonnement, montrent que lorsque \(n\) croît indéfiniment, si \(P\) n'est pas ...
Erdős, Pál, Turán, Pál
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On the distribution of r-full primitive roots
Proceedings - Mathematical Sciences, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Laohakosol, Vichian +2 more
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Distribution of roots of random polynomials
Physical Review Letters, 1992Summary: We consider polynomials of high degree with random coefficients which appear in the context of ``quantum chaotic'' dynamics and investigate various conditions under which their roots tend to concentrate near the unit circle in the complex plane. Correlation functions of roots are computed analytically.
Bogomolny, E., Bohigas, O., Leboeuf, P.
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Root distribution of fourVitis cultivars
Plant and Soil, 1983Root distribution of four Vitis cultivars at one location in Texas was asessed using trench profile and soil core sampling methods. Greater differences were obtained among cultivars utilizing the latter method when comparing root dry weights. Surface area of roots extracted from soil samples was estimated using a calcium nitrate slurry dip.
R. L. Perry, S. D. Lyda, H. H. Bowen
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