# Find Reimann zeta's zeros with SpecialFunctions and Roots

**URL:** https://discourse.julialang.org/t/find-reimann-zetas-zeros-with-specialfunctions-and-roots/61275
**Category:** Performance
**Created:** [May 17, 2021, 1:31am UTC](https://discourse.julialang.org/t/find-reimann-zetas-zeros-with-specialfunctions-and-roots/61275 "2021-05-17T01:31:50Z")
**Posts on this page:** 3
**Page:** 1

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### Author: ![Wei\_Yang](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/wei_yang/32/23951_2.png) [@Wei\_Yang](https://discourse.julialang.org/u/Wei_Yang)
#### Post date: [May 17, 2021, 1:31am UTC](https://discourse.julialang.org/t/find-reimann-zetas-zeros-with-specialfunctions-and-roots/61275/1 "2021-05-17T01:31:50Z")

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To find the zeros of the Reimann \zeta with real part 1/2, and imaginary part less than 1000 in norm, the following is what I’m using at the moment,

```julia
using SpecialFunctions
using Roots
g(x) = abs(zeta(.5 + x*im))

Z =[]
for i in 1:5:1000
    append!(Z,find_zeros(g,i,i+5))
end

E=[-reverse(Z)...,Z...] # by symmetric

```

I’m breaking the line `[0,1000]` into segments since `find_zeros(g,0,1000)` will miss many of the zeros.  
But this looks a bit awkward, I wonder what will be a better way to find the zeros.

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<div class="post-metadata">

### Author: ![Oscar\_Smith](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/oscar_smith/32/25343_2.png) [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)
#### Post date: [May 17, 2021, 1:48am UTC](https://discourse.julialang.org/t/find-reimann-zetas-zeros-with-specialfunctions-and-roots/61275/2 "2021-05-17T01:48:23Z")

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You might be interested in [roots interface · IntervalRootFinding.jl](https://juliaintervals.github.io/IntervalRootFinding.jl/latest/roots/). It has a few methods that can give rigorous proofs of no zeros in regions.

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<div class="post-metadata">

### Author: ![Wei\_Yang](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/wei_yang/32/23951_2.png) [@Wei\_Yang](https://discourse.julialang.org/u/Wei_Yang)
#### Post date: [May 17, 2021, 2:11am UTC](https://discourse.julialang.org/t/find-reimann-zetas-zeros-with-specialfunctions-and-roots/61275/3 "2021-05-17T02:11:13Z")

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I was not aware of this package. It appears that complex root finding is not yet implemented, but definitely a powerful package. Thank you 😃  
[https://github.com/JuliaIntervals/IntervalRootFinding.jl/issues/147](https://github.com/JuliaIntervals/IntervalRootFinding.jl/issues/147)