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2:The error term in Riemann–von Mangoldt formula (in wikipedia.org) is larger than 1. $\left|N(T)-\left(\frac{T}{2\pi}\log\frac{T}{2\pi e}-\frac{7}{8}\right)\right|<0.137\log T+0.443\log\log T+4.350,\text{ for } T>2.$. How do we use $N(T)$ from this formula to compare the number of numerical zeros from 1:?
@DenisSerre: Could you list explicitly the reference papers that you mentioned above for Navier-Stokes equations and for Euler equations ? Thanks a lot!
@AlexGavrilov: You may wish to look at this recent preprint (arxiv.org/abs/1706.08868). It concerns the zeros of the entire functions as Fourier transforms. The basic complex analysis method used there is based on the approach of Polya and Hurwitz. It is purely analytic because primes do not appear in the preprint.
