Some estimates of the \(H_{\infty}\)-uniform distribution. (English) Zbl 0624.10040

Schatte, Peter

Monatsh. Math. 103, 233-240 (1987).

The sequences \((y_ n)=(a+b \log n+\epsilon_ n)\) are uniformly distributed in the sense of the summation method \(H_{\infty}\). In the present paper the speed of convergence of this procedure is estimated for these sequences and for some other sequences. For the sequences \((a+b \log n)\) the \(H_{\infty}\)-means converge considerably faster than logarithmic means.

MSC:

11K06	General theory of distribution modulo \(1\)
40G99	Special methods of summability

Keywords:

H\({}_{\infty }\)-uniform distribution; summation method \(H_{\infty }\); speed of convergence; \(H_{\infty }\)-means

References:

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