“Prime Zeta Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

Prime Zeta Function

释义

Prime Zeta Function

The prime zeta function

(1)

where the sum is taken over Primes is a generalization of the Riemann Zeta Function

(2)

where the sum is over all integers. The prime zeta function can be expressed in terms of the Riemann Zeta Functionby


			(3)

Inverting then gives

(4)

where

is the Möbius Function. The values for the first few integers starting with two are

See also Möbius Function, Riemann Zeta Function, Zeta Function

References

Hardy, G. H. and Weight, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Oxford University Press, pp. 355-356, 1979.

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