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Posers and Puzzles

Posers and Puzzles

  1. Standard member royalchicken
    08 Aug '03 00:53 / 3 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....