On Wed, May 8, 2019 at 3:34 PM Mike Stay <metaweta@gmail.com> wrote:
On Wed, May 8, 2019 at 2:10 PM Dan Asimov <dasimov@earthlink.net> wrote:
Does an "arithmetic function" take its values in Z ?
It seems I've confused arithmetic fn with multiplicative fn. An arithmetic function is any function f(n) whose domain is the positive integers and whose range is a subset of the complex numbers, so my "in other words" is not the same as the first question I asked. It looks like I can use the formula here to extract the coefficients: https://mathoverflow.net/questions/329980/extracting-dirichlet-series-coeffi... but there's no guarantee that the resulting a(n) are a multiplicative function, so there's no guarantee that the coefficients can be "unpacked" into a bunch of OGFs.
Thanks!
Are there results about when a Dirichlet series is multiplicative? Like (just guessing here) all its complex zeros are confined to the critical strip? -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com