02/27/2023, 01:18 PM
Since we are talking about special dirichlet series , I want to mention this special function again
f(s) = sum (a_n)^(-s)
where a_n is the binary partition function.
(binary partition zeta function or so )
since the binary partition grows faster than polynomial ( yet much slower than exp or even semi-exp ,more like n^ln(n) )
we get that
f(s) converges for Re(s) > 0.
Typical questions occur ; zero's , continuation to Re(s) < 0 , reflection ? natural boundary ?? etc
Im not sure if we have a summability method yet for Q = a_1 + a_2 + a_3 + ...
Can we just go around the pole at 0 , or are there issues ??
Does it have number theoretical or combinatorical meanings ?
regards
tommy1729
" Truth is what does not go away when you stop believing in it "
Tom Marcel Raes
f(s) = sum (a_n)^(-s)
where a_n is the binary partition function.
(binary partition zeta function or so )
since the binary partition grows faster than polynomial ( yet much slower than exp or even semi-exp ,more like n^ln(n) )
we get that
f(s) converges for Re(s) > 0.
Typical questions occur ; zero's , continuation to Re(s) < 0 , reflection ? natural boundary ?? etc
Im not sure if we have a summability method yet for Q = a_1 + a_2 + a_3 + ...
Can we just go around the pole at 0 , or are there issues ??
Does it have number theoretical or combinatorical meanings ?
regards
tommy1729
" Truth is what does not go away when you stop believing in it "
Tom Marcel Raes