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Über die Größenordnung der Teilerfunktion in Restklassen

On the order of magnitude of the divisor function in residue classes

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Abstract

Letd(n) denote the number of divisors ofn, then the asymptotic formula

$$\sum\limits_{\mathop {n< x}\limits_{n = r(\bmod m)} } {d(n) = \xi _1 (r,m)} x\log x + \xi _2 (r,m)x + O(x^{1/2} )$$

is derived and, as the main result of the paper, the coefficients ξi(rm),i= 1,2, as functions of the powers of the prime numbers ofm and of g. c. d. (r, m) are determined.

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Literatur

  1. Lehmer, D. H.: Euler constants for arithmetical progressions. Acta Arithm.27, 125–142 (1975).

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  2. Hardy, G. H., undE. M. Wright: Einführung in die zahlentheorie. München: Oldenbourg. 1958.

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Kopetzky, H.G. Über die Größenordnung der Teilerfunktion in Restklassen. Monatshefte für Mathematik 82, 287–295 (1976). https://doi.org/10.1007/BF01540600

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  • DOI: https://doi.org/10.1007/BF01540600

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