[special] binary partition zeta function - Printable Version +- Tetration Forum (https://tetrationforum.org) +-- Forum: Tetration and Related Topics (https://tetrationforum.org/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://tetrationforum.org/forumdisplay.php?fid=3) +--- Thread: [special] binary partition zeta function (/showthread.php?tid=1719)

[special] binary partition zeta function - tommy1729 - 02/27/2023 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 RE: [special] binary partition zeta function - tommy1729 - 02/27/2023 see : https://math.eretrandre.org/tetrationforum/showthread.php?tid=911 regards tommy1729