My Math Forum Riemann Hypothesis.

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 October 31st, 2013, 12:54 AM #1 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Riemann Hypothesis. In Atle Selberg's result, i.e., $N_0(T) \gg T \log T$, he considers using a mollificated eta which in turn the eta but multiplied by a mollifier, namely, a Dirichlet polynomial, i.e., $\psi(s)= \sum_{d \leq D} h$$\frac{\log \,d}{\log \, D}$$ a_n d^{-s}$ where $h(x)$ 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 $\zeta^{-1/2}$. The factor he uses is the square of this function, evidently to ignore the sign changes coming from the zeros of $\psi$. I was wondering, how much knowledge we have of the behavior of $\psi$, especially, the zeros?

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