Loading [MathJax]/jax/output/HTML-CSS/jax.js

First time here? Check out the FAQ!

Ask Your Question
1

Solving zeta function equation numerically

asked 8 years ago

ec92 gravatar image

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

I tried

 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.

Preview: (hide)

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 gravatar imageslelievre ( 8 years ago )

1 Answer

Sort by » oldest newest most voted
2

answered 8 years ago

If you plot your function first, for example with

f = diff(zeta(x))/zeta(x)+.75
plot(f,0,10,ymin=-5,ymax=5,detect_poles=True,figsize=[4,3])

you can see approximately where the zero is:

image description

You just need to change the range over which you're searching:

find_root(f,0,10)
1.8333259941894324

Here's a link to live example.

Preview: (hide)
link

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower

Stats

Asked: 8 years ago

Seen: 702 times

Last updated: Jun 01 '16