On Wed, May 8, 2019 at 5:18 PM Brad Klee <bradklee@gmail.com> wrote:
On Wed, May 8, 2019 at 12:01 PM Mike Stay <metaweta@gmail.com> wrote:
In other words, given ordinary generating functions A_i(x) = sum_{n >= 0} a^i_n x^n, I can combine them into a Dirichlet generating function A(s) = prod_{i >= 1} A_i(p_i^{-s}).
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Unless I am mistaken, this is a valid argument saying that your suggested product formulas generally do not exist.
I'm just talking about https://en.wikipedia.org/wiki/Bell_series . I agree that an arbitrary function interpreted as a Dirichlet series will not give rise to a multiplicative function in general. Are there results on when it does? -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com