J. van de Lune, H. J. J. te Riele, D. T. Winter, On the Zeros of the Riemann Zeta Function in the Critical Strip IV, Math. Comp., 46, 1986, p.667-681. Home/Search Document Not in Database Summary Related Articles |
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On the Number of Prime Numbers less than a Given Quantity - Kolev (2000) (Correct)
.... showed in [22] that at least 1 3 (as a ratio to N (T ) of the roots must lie on #z = 1 2, a result which has since been sharpened to 40 by Conrey in 1989 (see [34] Computational results from 1986 show, that the first 1, 500, 000, 001 non trivial zeros do indeed have real part one half (see [24]) However, the main conjecture in the field, that there are no other roots, stays unproven. Another interesting point is the study of #(z) at the integers. Euler computed #(2k) for k = 1 . 13: #(2) # 2 6 , #(4) # 4 90 , see homework #4) For n even integer it is known, ....
J. van de Lune, H. J. J. te Riele, D. T. Winter, On the Zeros of the Riemann Zeta Function in the Critical Strip IV, Math. Comp., 46, 1986, p.667-681.
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