Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Sunday, January 11, 2009

Riemann Products II

The consideration of ordinals $N = p_1 p_2 p_3 \cdots p_k$, where all prime factors $p_i$ are distinct, occurs as the Pauli exclusion principle for the Riemann gas, whose partition function is the Riemann zeta function.

The product expression for the inverse zeta function is always well defined for finite products, which define a sequence of functions $\zeta_N$ for $N$ such a Pauli ordinal. Showing that the limit $N \rightarrow \infty$ leads to a well defined zeta function for basically all $s$ values is equivalent to the Riemann hypothesis.


Anonymous Anonymous said...

Well, I have no idea what Riemann Products is/are.... but how are you Marni? Finally some nice weather here in Wanaka. Will you get a chance to go for any walks while you are waiting? Remember the nice adventure we had on the Port Hills?
Have a nice day, Kerie

January 11, 2009 12:51 PM  
Blogger Kea said...

Hi Kerie! Yes, we have had some good adventures! And I should be walking in the Port Hills. But I'm not.

January 11, 2009 2:56 PM  

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