On Sep 13, 10:01 am, "Rod" <rodrodrod...@hotmail.com> wrote: > "Greg Neill" <gneil...@MOVEsympatico.ca> wrote in message > > news:BUpjo.firstname.lastname@example.org... > > > > > > > Robert Adams wrote: > >> I could use a little help trying to solve the following engineering > >> problem (no, I am not a student looking for homework help!) > > >> I need to find the values of w which cause the following summation to > >> go to zero > > >> sum (n = 1 to N) of exp(-i*w*ln(n)) > > >> where i is the usual sqrt(-1) > > >> For a given N, there are infintely many solutions due to the > >> periodicity of exp(-i ...) > >> How do I find these solutions? > > >> Thanks for any pointers. > > >> Bob Adams > > > Have you looked into expanding the exponentials into > > trig form? You'll then have a sum of cos and > > imaginary sin terms which will each have to sum to > > zero separately. > > That's my approach as well > Wouldn't w have to be complex to achieve both series being zero. > > Is this not a truncated zeta function?- Hide quoted text - > > - Show quoted text -
Yes, this is related to the zeta function.
I was hoping to to find a solution where w is real, but this may not be possible as you point out