在文献[1～3]中研究了同Siegel E,G函数有关的代数方程根的丢番图逼近.本文给出同F函数有关的一个丢番图逼近定理.令K是次数为d的代数数域,O_k为K上整数环.定义F函数:幂级数f(z)=sum from n-0 to ∞ (a_n n!)z^n满足条件:(1)对所有n,α_...在文献[1～3]中研究了同Siegel E,G函数有关的代数方程根的丢番图逼近.本文给出同F函数有关的一个丢番图逼近定理.令K是次数为d的代数数域,O_k为K上整数环.定义F函数:幂级数f(z)=sum from n-0 to ∞ (a_n n!)z^n满足条件:(1)对所有n,α_n∈K和(?)≤c_1~n(?)表示α和所有共轭的绝对值的最大值);(2)存在自然数序列{d_l},d_1=q_0~l(d_(0l))使得d_l α_n∈O_k,n=0,1…,l,l=1,2,…,并且d_(0l)只被满足p≤c_2l的素数p整除,还有ord_(p)d_0l≤c_3logl.称f(z)属于F(K,c_1,C_2,c_3,q_0)类.有很多函数属于F函数类,例如超几何函数现在假设f_1(z)…,f(m)(z)∈F(K,c_1,c_2,c_3,q_0)类并满足线性微分方程组y_1~＇=sum from j=1 to m (A_(ij)(z)y_j,A_(ij)(z)∈C(z),i=1,…,n.)展开更多
1 .Introduotion Int 5 PaPer,we 8hall obtain omo lower estima er linear formg andPolynomial,in the values offunoion at algebraio Points.As usualdenotesan algebraio number field of
In his fundamental paper on E-functions in 1929, Siegd pointed out that his method could also be used to investigate G-functions. This suggestion of Siegel has been more recently followed by Nurmagomedov, Galochkin. F...In his fundamental paper on E-functions in 1929, Siegd pointed out that his method could also be used to investigate G-functions. This suggestion of Siegel has been more recently followed by Nurmagomedov, Galochkin. Flicker, V(?)n(?)nen, Matvejev and Xu, for examples but their results use the additional Galochkin’s condition which is usually展开更多
Since C. L. Siegel introduced E-functions aud G-functions in 1929, A. B. had developed Siegel’s method and established the Siegel-’s theory of E-functions. Recently, some mathematicians[3-6] discussed the algebraic ...Since C. L. Siegel introduced E-functions aud G-functions in 1929, A. B. had developed Siegel’s method and established the Siegel-’s theory of E-functions. Recently, some mathematicians[3-6] discussed the algebraic independence of the values of G-functions at the algebraic points around 0 gave the estimations of low bounds for polynomial forms, and obtained the p-adic form of such results. These estimations depend on the maximum of the coefficients of a展开更多
文摘在文献[1～3]中研究了同Siegel E,G函数有关的代数方程根的丢番图逼近.本文给出同F函数有关的一个丢番图逼近定理.令K是次数为d的代数数域,O_k为K上整数环.定义F函数:幂级数f(z)=sum from n-0 to ∞ (a_n n!)z^n满足条件:(1)对所有n,α_n∈K和(?)≤c_1~n(?)表示α和所有共轭的绝对值的最大值);(2)存在自然数序列{d_l},d_1=q_0~l(d_(0l))使得d_l α_n∈O_k,n=0,1…,l,l=1,2,…,并且d_(0l)只被满足p≤c_2l的素数p整除,还有ord_(p)d_0l≤c_3logl.称f(z)属于F(K,c_1,C_2,c_3,q_0)类.有很多函数属于F函数类,例如超几何函数现在假设f_1(z)…,f(m)(z)∈F(K,c_1,c_2,c_3,q_0)类并满足线性微分方程组y_1~＇=sum from j=1 to m (A_(ij)(z)y_j,A_(ij)(z)∈C(z),i=1,…,n.)
文摘1 .Introduotion Int 5 PaPer,we 8hall obtain omo lower estima er linear formg andPolynomial,in the values offunoion at algebraio Points.As usualdenotesan algebraio number field of
文摘In his fundamental paper on E-functions in 1929, Siegd pointed out that his method could also be used to investigate G-functions. This suggestion of Siegel has been more recently followed by Nurmagomedov, Galochkin. Flicker, V(?)n(?)nen, Matvejev and Xu, for examples but their results use the additional Galochkin’s condition which is usually
文摘Since C. L. Siegel introduced E-functions aud G-functions in 1929, A. B. had developed Siegel’s method and established the Siegel-’s theory of E-functions. Recently, some mathematicians[3-6] discussed the algebraic independence of the values of G-functions at the algebraic points around 0 gave the estimations of low bounds for polynomial forms, and obtained the p-adic form of such results. These estimations depend on the maximum of the coefficients of a
