Spectral interpretation of Primes

**zetafunction** · Jun21-09, 07:23 AM

the idea is

is there a Linear operator L so $LaTeX Code: L | \\phi _n > =p_n |\\phi_n >$

with p_n being the nth prime and L a linear operator , is it possible to have an spectral interpretation for prime numbers ?

**ramsey2879** · Jun21-09, 10:14 AM

Originally Posted by zetafunction

the idea is

is there a Linear operator L so $LaTeX Code: L | \\phi _n > =p_n |\\phi_n >$

with p_n being the nth prime and L a linear operator , is it possible to have an spectral interpretation for prime numbers ?

I don't think your formula makes sense, but I am not sure. It looks like you have L and p(n)each divide $LaTeX Code: \\phi_n$ but should that really be so since $LaTeX Code: \\phi_n$ should be less than p(n)?
PS There are over 20,000 articles in science direct that combined the words spectral and primes. Some mention a spectral analysis of the prime intevals etc., but I dont have access to the specific articles.