This article is cited in 9 papers

On estimates, unimprovable with respect to height, of some linear forms

A. I. Galochkin


Abstract: Lower and upper bounds that differ from each other only by a constant factor are obtained for linear forms in values of the function
$$ \psi(z)=\sum_{\nu=0}^\infty\frac{z^\nu}{b^{(s+1)\nu}\nu!\,[\lambda_1+1,\nu]\dots[\lambda_s+1,\nu]}, $$
$[\lambda+1,\nu]=(\lambda+1)\dots(\lambda+\nu)$, $[\lambda+1,0]=1$ and its $s$ successive derivatives at the point $z=\frac1b$ under the condition that $a,b$ and $a\lambda_1,\dots,a\lambda_s$ are integers in some imaginary quadratic field.
Bibliography: 9 titles.

UDC: 511.8

MSC: 10C02, 10F10

Received: 09.03.1983

 English version: Mathematics of the USSR-Sbornik, 1985, 52:2, 407–421

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