- #1
sparsh12
- 12
- 0
I don't know anything of complex analysis or analytic number theory or analytic continuation. But i read about zeta function and riemann hypothesis over wikipedia, clay institute's website and few other sources. I started with original zeta function
http://img600.imageshack.us/img600/7184/86023001.jpg
and then for complex s of form a+ib, where a and b are real,it would be
http://img839.imageshack.us/img839/2746/62003747.jpg
Then i did few things and it became,
http://img706.imageshack.us/img706/879/19378823.jpg
It can be observed that above relation is actually,
http://img716.imageshack.us/img716/3409/42615034.jpg
and if reimann hypothesis is true, first term diverges in above equation, which would in turn mean second term must tend to -∞.
Now my questions are:
1)Am i on right path? I have plans to start real and complex analysis soon. Would above progress be useful?
2)Has anyone around got any idea of proving second term tending to -∞ without assuming riemann hypothesis true? Won't this method help prove reimann hypothesis true? As far as i understand, all solutions of above zeta function satisfies riemann zeta function(one of analytic continuation).
If i talked nonsense above, please rectify me.
http://img600.imageshack.us/img600/7184/86023001.jpg
and then for complex s of form a+ib, where a and b are real,it would be
http://img839.imageshack.us/img839/2746/62003747.jpg
Then i did few things and it became,
http://img706.imageshack.us/img706/879/19378823.jpg
It can be observed that above relation is actually,
http://img716.imageshack.us/img716/3409/42615034.jpg
and if reimann hypothesis is true, first term diverges in above equation, which would in turn mean second term must tend to -∞.
Now my questions are:
1)Am i on right path? I have plans to start real and complex analysis soon. Would above progress be useful?
2)Has anyone around got any idea of proving second term tending to -∞ without assuming riemann hypothesis true? Won't this method help prove reimann hypothesis true? As far as i understand, all solutions of above zeta function satisfies riemann zeta function(one of analytic continuation).
If i talked nonsense above, please rectify me.
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