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log-s-s-1-J-x-x-s-1-dx-Prove-that-Here-J-x-pi-x-1-2-pi-x-1-3-pi-x-1-3-pi-x-Prime-counting-function-

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Question Number 141345 by Dwaipayan Shikari last updated on 17/May/21
((log(ζ(s)))/s)=∫_1 ^∞ J(x)x^(−s−1) dx ( Prove that) Here J(x)=π(x)+(1/2)π((√x))+(1/3)π((x)^(1/3) )+... π(x):=Prime counting function
log(ζ(s))s=∫1∞J(x)x−s−1dx(Provethat)HereJ(x)=π(x)+12π(x)+13π(x3)+…π(x):=Primecountingfunction

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