The above plot shows
 for  between 0 and 60. As can be seen, the first few nontrivial zeros occur at the values given in the following table (Wagon 1991, pp. 361-362 and 367-368; Havil 2003, p. 196; Odlyzko), where the corresponding negative values are also roots. The integers closest to these values are 14, 21, 25, 30, 33, 38, 41, 43, 48, 50, ... (OEIS A002410). The numbers of nontrivial zeros less than 10,  ,  , ... are 0, 29, 649, 10142, 138069, 1747146, ... (OEIS A072080; Odlyzko).
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Monday, January 29, 2018
14.13i............could be seen as both e and pi.....................14.13i...........14 + 13.....= 27.............e starts out...........2.7..............the 13 is under the dec point............pi starts out........3.14.............the beg to middle........end to middle............14 is 14........0.13i.........is 0.13.......is 13..........from end to middle.....31.........over lap the 1's...................and u have the beg of pi.......fractal patterns.......chaos theory...........
The 1st zero is like e and pi......
Riemann Zeta Function Zeros Zeros of the Riemann zeta function  come in two different types. So-called "trivial zeros" occur at all negative even integers  ,  ,  , ..., and "nontrivial zeros" occur at certain values of  satisfying
 in the "critical strip"  . In general, a nontrivial zero of  is denoted  , and the  th nontrivial zero with  is commonly denoted  (Brent 1979; Edwards 2001, p. 43), with the corresponding value of  being called  . Wiener (1951) showed that the prime number theorem is literally equivalent to the assertion that  has no zeros on  (Hardy 1999, p. 34; Havil 2003, p. 195). The Riemann hypothesis asserts that the nontrivial zeros of  all have real part ![sigma=R[s]=1/2](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vIBRrVkFKDBvVskL3bLeCRE_Mz6oXxHh_fY0EgB2m--R2s6HGRAdoifaYpcsPmvC7OzAQ0ojcU9mFlo99bYnJaA9zmPylF2zb3_xKh-A469759GZ-ek1zMvuXJ8RQtvR86V6Y4lVQQOCgZ5L3Nhc-7L0YW2UN1=s0-d) , a line called the "critical line." This is known to be true for the first  zeros.  An attractive poster plotting zeros of the Riemann zeta function on the critical line together with annotations for relevant historical information, illustrated above, was created by Wolfram Research (1995).
 plotted in the complex plane together with the complex modulus of  . As can be seen, in right half-plane, the function is fairly flat, but with a large number of horizontal ridges. It is precisely along these ridges that the nontrivial zeros of  lie.  The position of the complex zeros can be seen slightly more easily by plotting the contours of zero real (red) and imaginary (blue) parts, as illustrated above. The zeros (indicated as black dots) occur where the curves intersect.  The figures above highlight the zeros in the complex plane by plotting  (where the zeros are dips) and  (where the zeros are peaks).  The above plot shows for between 0 and 60. As can be seen, the first few nontrivial zeros occur at the values given in the following table (Wagon 1991, pp. 361-362 and 367-368; Havil 2003, p. 196; Odlyzko), where the corresponding negative values are also roots. The integers closest to these values are 14, 21, 25, 30, 33, 38, 41, 43, 48, 50, ... (OEIS A002410). The numbers of nontrivial zeros less than 10, , , ... are 0, 29, 649, 10142, 138069, 1747146, ... (OEIS A072080; Odlyzko).
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Everyone knows..........but no one does anything except to stare at my penis......and testicles......which is sexual harassment........but it is ok in the USA.........b/c women are involved....
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