Introduction :

This thread is dedicated to discuss about Hardy-Littlewood's estimate of the $ \displaystyle N_0(T)$, i.e., the number of critical zeros of the Riemann zeta function with imaginary part smaller than $ \displaystyle T + 1$. The final result of Hardy-Littlewood estimate shows that there are infinitely many zeros of zeta that lies in the critical line.

This thread would be continued in more than one post, each of them showing different lemmas. The estimated number of post required would be 8 or less. There could be prolonged gaps in between the posts which are to be continued, so it would certainly be disappointing not to be able to look at it all at once; but I think a serious subject like this could take days to digest, so go slow and you won't throw up! Nevertheless, I think this note would be of particular interest once completed.

And as a final note, I would be putting it up altogether in a very short, less elegant and more understandable format. I have put quite a few things from here and there, so there could possibly be many typos. I hope members of MHB would certainly help me to point those out.

The commentary thread for this note is here :

Balarka

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