Posers and Puzzles

Posers and Puzzles

  1. Standard memberroyalchicken
    CHAOS GHOST!!!
    Elsewhere
    Joined
    29 Nov '02
    Moves
    17317
    08 Aug '03 00:533 edits
    Let z be a complex number. Let

    S(z) = 1 + 2^-z + 3^-z + 4^-z + ....

    Show that all the zeros of this function are either negative even integers or of the form 1/2 + it. Enjoy 😛!

    EDIT I have no idea how to come up with a solid proof...and I've tried.

    EDIT THE SECOND My sarcastic streak strikes again! Either try this question or look it up to see why....