“Mertens Constant”的概念、定义、习题解题方法及翻译-数学辞典

单词

Mertens Constant

释义

Mertens Constant

A constant related to the Twin Primes Constant which appears in the Formula for the sum of inverse Primes

(1)

which is given by

(2)

Flajolet and Vardi (1996) show that

(3)

where

is the Euler-Mascheroni Constant,

is the Riemann Zeta Function, and

is theMöbius Function. The constant

also occurs in the Summatory Function of the number ofDistinct Prime Factors,

(4)

(Hardy and Wright 1979, p. 355).

The related constant

(5)

appears in the Summatory Function of the Divisor Function

(6)

(Hardy and Wright 1979, p. 355).

See also Brun's Constant, Prime Number, Twin Primes Constant

References

Flajolet, P. and Vardi, I. ``Zeta Function Expansions of Classical Constants.'' Unpublished manuscript. 1996. http://pauillac.inria.fr/algo/flajolet/Publications/landau.ps.

Hardy, G. H. and Weight, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Oxford University Press, pp. 351 and 355, 1979.

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