Hi, I was playing with Riemann zeta function on mathematica. I encountered with a quite interesting result. I iterated Riemann zeta function for zero. (e.g Zeta...[Zeta[Zeta[0]]]...] It converges into a specific number which is -0.295905. Also for any negative values of Zeta function, iteration results the same number.(adsbygoogle = window.adsbygoogle || []).push({});

I searched on internet, but I couldn't find any thing about it, besides one review text.

What is the meaning of that number? for s≤0, Zeta iteration converges to a number. Is that something important?

On the other hand, a lot of great mathematicians dealed with Riemann zeta function and i'm sure they have reached this result, and since nowhere mentions that, it may be too obvious or trivial. But I'm just curious about it. Can someone inform me?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# About interesting convergence of Riemann Zeta Function

**Physics Forums | Science Articles, Homework Help, Discussion**