If you enter a non-trivial zero value in x, the value of the equation is zero.

Transcription

1 Original article Riemann hypothesis seems correct Toshiro Takami April 10, 2019 Abstract If you enter a non-trivial zero value in x, the value of the equation is zero. The above equation is derived from cos(π/3)=0.5 after trial and error, and as a result of many examinations, it turned out that this equation is correct. And it turned out that the same result can be obtained by putting sin instead of cos. This also performed a number of inspections. And, c=0.5 is best. converge. If you use or instead of 0.5, it will not 1

2 And when a non-trivial zero value is entered, the tendency to converge to 0 is seen, but if the non-trivial zero value is shifted even by 0.01, the tendency to converge generally tends to disappear. If you add it to infinity instead of 10000, it will converge to 0. Discussion It was calculated as far as possible by programming. We tried with not only but also various non-trivial zero values, all with the same trend. And there was no tendency to converge at the time of 0.49, 0.51 instead of 0.5. The intersection of the real and imaginary parts was considered to be x, and it was not possible to distinguish which of the real and imaginary parts is cos or sin. At first, 0.49 and 0.51 were used, but it was found that convergence did not occur even with and 0.501, and and were used from the latter half. Even at non-trivial zero values. It was too obvious at 0.01 and subtle at (chapter 1) In the following case, the disappearance of the tendency to converge to 0 is clear. sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.49 cos[ *ln(2n)]/(2n)^0.49} =

3 [ ]= [ ]= [ ]= not converge sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.499 cos[ *ln(2n)]/(2n)^0.499} [10000]= [100000]= [ ]= [ ]= [ ]= ????not converge sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.5 cos[ *ln(2n)]/(2n)^0.5} [ ]= [ ]= [ ]=

4 [ ]= converge In the following case, the disappearance of the tendency to converge to 0 is clear. sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.51 cos[ *ln(2n)]/(2n)^0.51 } [ ]= [ ]= [ ]= not converge (I replaced cos with sin.) sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.49 sin[ *ln(2n)]/(2n)^0.49 } [ ]= [ ]= [ ]= not converge 4

5 sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.5 sin[ *ln(2n)]/(2n)^0.5 } = [ ]= [ ]= [ ]= converge.. sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.499 sin[ *ln(2n)]/(2n)^0.499} [ ]= [ ]=

6 [ ]= [ ]= not converge sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.5 sin[ *ln(2n)]/(2n)^0.5 } [ ] = [ ] = [ ] = [ ]= converge?? sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.501 sin[ *ln(2n)]/(2n)^0.501 } [ ]= [ ]= [ ]= [ ]= not converge 6

7 .. sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.499 sin[ *ln(2n)]/(2n)^0.499} [ ]= [ ]= [ ]= not converge sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.50 sin[ *ln(2n)]/(2n)^0.50} [ ]= [ ]= [ ]= [ ]= converge??? 7

8 sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.501 sin[ *ln(2n)]/(2n)^0.501 } [ ]= [ ]= [ ]= [ ]= not converge.. sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.499 sin[ *ln(2n)]/(2n)^0.499} [10000]= [100000]= [ ]= [ ]= [ ]= ??? 8

9 sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.5 sin[ *ln(2n)]/(2n)^0.5} [10000]= [100000]= [ ]= [ ]= [ ]= [ ]= converge sum_{n=1}^{10000}{sin[ *ln(2n-1)]/(2n-1)^0.501 sin[ *ln(2n)]/(2n)^0.501} [10000]= [100000]= [ ]= [ ]= [ ]= [ ]= ????? 9

10 sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.499 sin[ *ln(2n)]/(2n)^0.499} [ ]= [ ]= [ ]= [ ]= not converge sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.50 sin[ *ln(2n)]/(2n)^0.50} [ ]= [ ]= [ ]= converge sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.501 sin[ *ln(2n)]/(2n)^0.501} [ ]= [ ]= [ ]= not converge 10

11 sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.499 sin[ *ln(2n)]/(2n)^0.499} [ ]= [ ]= [ ]= not converge sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.50 sin[ *ln(2n)]/(2n)^0.50} [ ]= [ ]= [ ]= converge sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.501 sin[ *ln(2n)]/(2n)^0.501} [ ]= [ ]= [ ]= [ ]= not converge (chapter 2) In the following case, the disappearance of the tendency to converge to 0 is clear. 11

12 If switch to sin instead of cos, the disappearance of the tendency to converge to 0 is clear. ( = ) ( is non-trivial zero value.) sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.5 sin[ *ln(2n)]/(2n)^0.5 } [ ]= [ ]= [ ]= not converge??? change sin to cos. ( = ) ( is non-trivial zero value.) sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.5 cos [ *ln(2n)]/(2n)^0.5 } [10000]= [100000]= [ ]= [ ]= [ ]= [ ]= not converge 12

13 ( = ) sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.5 cos[ *ln(2n)]/(2n)^0.5 } [10000]= [100000]= [ ]= [ ]= [ ]= not converge ( = ) sum_{n=1}^{1000}{sin[ *ln(2n-1)]/(2n-1)^0.5 sin[ *ln(2n)]/(2n)^0.5 } [10000]= [100000]= [ ]= [ ]=

14 [ ]= not converge ( = ) sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.5 cos[ *ln(2n)]/(2n)^0.5 } [ ]= [ ]= [ ]= not converge ( is non-trivial zero value.) sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.5 cos[ *ln(2n)]/(2n)^0.5 } [ ]= [ ]= [ ]= converge ( = ) sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.5 cos[ *ln(2n)]/(2n)^0.5 } [ ]= [ ]=

15 [ ]= not converge ( is non-trivial zero value.) sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.5 cos[ *ln(2n)]/(2n)^0.5 } S( )= S( )= S( )= S( )= converge ( = ) sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.5 cos[ *ln(2n)]/(2n)^0.5 } [ ]= [ ]= [ ]= not converge 15

16 ( = ) sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.5 cos[ *ln(2n)]/(2n)^0.5 } [ ]= [ ]= [ ]= [ ]= not converge ( is non-trivial zero value.) sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.5 cos[ *ln(2n)]/(2n)^0.5 } [ ]= [ ]= [ ]= converge ( = ) sum_{n=1}^{1000}{cos[ *ln(2n-1)]/(2n-1)^0.5 cos[ *ln(2n)]/(2n)^0.5 } [ ]= [ ]= [ ]= not converge 16

17 References 1. Riemann, Bernhard, Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse. (1859), John Derbyshire, Prime Obsession: Bernhard Riemann and The Greatest Unsolved Problem in Mathematics, Joseph Henry Press,(2003), ISBN Toshiro Takami, Simulation of Nontribial Zero Point of Riemann Zeta Function. vixra: Toshiro Takami, Consideration of Riemann Hypothesis 43 Counterexamples. vixra: Toshiro Takami, Riemann Hypothesis 43 Counterexamples, vixra: Toshiro Takami, Next Infinite is Zero, vixra: I am a psychiatrist now and also a doctor of brain surgery before. mmm82889@yahoo.co.jp 17

18 I would like to receive an . I will not answer the phone. Currently 57 years old. Born on November 26, 1961 (Home) Toshiro Takami 47-8 kuyamadai, Isahaya City, Nagasaki Prefecture, Japan (postscript) Prize money for my son and daughter. 18

19 2019/04/10 10:50

20 2019/04/10 10:50