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October 31st, 2013, 01:54 AM   #1
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Riemann Hypothesis.

In Atle Selberg's result, i.e., , he considers using a mollificated eta which in turn the eta but multiplied by a mollifier, namely, a Dirichlet polynomial, i.e.,

where is a real and continues function on the interval [0, 1] which is both 1 + O(x) and O(1 - x) and the constants are the coefficients of Dirchlet expansion of .

The factor he uses is the square of this function, evidently to ignore the sign changes coming from the zeros of .

I was wondering, how much knowledge we have of the behavior of , especially, the zeros?
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