Recent content by rlrandallx

Thanks for all the helpful remarks. I learned a lot! I was trying to build off of Hardy's (1914) results. He extended the zeta function to one where 0< Re[s] <1 and found f(1-s) = f(s) and as I understood it, all the non-trivial zeroes were the same as that for the zeta Riemann function. In...

Is sum ( k^(1-s) - k^(s) ) / k ) analytic continuous for 0< Re(s) <1, pos. k ? in the complex plane? For s=.4 => sum ( k^.6 - k^.4)/k = (k'-k'')/k would seem close to zero for most terms. For k=10 k^(.6)= 3.98, k^(.4)=2.5 , k'-k''=3.58 => 0.358 for term 10. For k=100=...

If (A*i)^2 = -A^2 (i^2= -1) Then SQT(1/4 - A^2) could be < 1 if e.g. A^2 = 1/9, but I get what you are saying and now am working with XI(s) which is convergent and continuos. If 0 = xi(1-s) = xi(s) 0 < s < 1, Hardy 1914 and xi(s) is convergent, continuous and has the same...

Why does the series converge to 0 if s=1/2? -rlrandallx

So the constraint is that 0 < s < 1 . For Re[s] = 1/2 , Re[s] > 0 (not 1.) On the "flaw" I'm saying IF there exists s' s. t. (k^(1-s') - k^(s'))/k = 0 for k=1-> oo then k^(1-s') - k^(s')=0 and only s'=1/2 makes this true. So for s'=1/2 every term is 0 for all k shown above. So for...

Sorry, The below paragraph was supposed to be above the proof. (excuse free use of 's'): We will try to prove that the nontrivial or interesting Riemann zeta function zeros, i.e., the values of other than -2, -4, -6, ... such that Z(s)=0 (where Z(s) is the Riemann zeta function) all...

Hi, I am attempting to prove Riemann's Hypothesis and need someone to critque the proof. 1. Does it prove anything? 2. What more must I prove? 3. Where can I learn more about this problem? See attached 51910_RH_proof.JPG