Solving zeta function equation numerically

numerical_approx
zeta
derivative

asked 2016-06-01 01:07:50 +0200

ec92
33 ●2 ●4 ●8

I'm trying to solve the equation $$ \zeta'(x)/\zeta(x) = - 3/4 $$ numerically. I'm expecting/hoping for an answer between 1 and 10.

I tried

$\texttt{ find_root(diff(zeta(x))/zeta(x) + 0.75, 2, 40)}$,

but this returns 0.0. I don't know what that ratio of zeta functions looks like, so it's possible there isn't a root, but I don't see why I'm getting an answer outside the specified interval.

Can anyone help find the true root? Thanks.

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Comments

What version of Sage are you using? I get the following in Sage 7.2:

sage: find_root(diff(zeta(x))/zeta(x)+.75, 2, 40)
Traceback (most recent call last):
...
RuntimeError: f appears to have no zero on the interval

slelievre ( 2016-06-01 06:12:21 +0200 )edit

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