Zeros of polynomials in several variables and fractional order differences of their coefficients

Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1964-07-01 DOI:10.6028/JRES.068B.017

B. Mond, O. Shisha

引用次数: 1

Abstract

where (J" is the set of all sequences of integers (hI, . "hp) with 0 ~ hv ~ nv + 1, v = 1, 2" , "p, (hi" . ,hp)=Io(O" . ,0), Setting ZI = Z2 = , , ,= Zp = 1, we have PCo, , ,0 =-L (VCh] , , , hp), and (h, . ... , hp)w thus (p -J'~ Zj) E (zJ" , ., zp)=o L('V Chi, , , hp)z1l, . ,z~p -1), from which we infer that V Chl ' , ' hp (h" . , " hp)'CT =10 0 for at least one (hi ' , ,hp)€(J", If Izvl < 1 for v = 1, 2, ' . " p then

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若干变量多项式的零点及其系数的分数阶差

其中(J”是所有整数序列(hI，。)的集合。“惠普)0 ~高压~ nv + 1, v = 1, 2”,“p,(嗨”。惠普)= Io (O”。, 0),设置子= Z2 = , , ,= PCo Zp = 1,,,, 0 = - l (VCh),惠普)和(h,……因此,hp) w (p - j ~ Zj) E (Zj”,zp) = o L(“惠普)z1l V气,,,,。，z~p -1)，由此我们推断出V Chl '， ' hp (h '。， " hp)' < 0 =至少一个(hi '，，hp)€(J '， If Izvl < 1 for v = 1,2， ';“那么。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics

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