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Old 2020-10-14, 16:56   #1
Dec 2018

29 Posts
Default Help to find the non-integer roots of this "prime" equation

MODERATOR NOTE: Moved from Lounge.

Hello, I am having a hard time (and possibly will never figure out) trying to find out the non-prime roots of the equation:

\frac{\Lambda(n)}{\log{n}}=-2\sum_{i=1}^{\infty} (-1)^i (2\pi n)^{2i}\sum_{j=1}^{i} \frac{(-1)^j (2\pi)^{-2j}\log{\zeta(2j)}}{(2i+1-2j)!}=1

This equation has integer roots at the primes, but I have no idea what the non-integer roots are, and perhaps this is as hard to figure as the roots of the Riemann zeta function.

Any takers? To make this easier, I am attaching a graph of this function, and I believe (an educated guess) this equation doesn't have non-real roots.
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Last fiddled with by Dr Sardonicus on 2020-10-15 at 11:33
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