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knowing the zeta function

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  • leavemsg1
    I wrote to Dr. Math on 9/6/06... today. He asked... What is your question? I wrote: I see the many definitions that math books are filled with and ponder- ed
    Message 1 of 2 , Sep 6, 2006
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      I wrote to Dr. Math on 9/6/06... today.

      He asked... What is your question?

      I wrote:

      I see the many definitions that math books are filled with and ponder-
      ed one myself. I call it the ideal zero asymmetrical range of a
      complex function. It happens only when the following condition is
      met. The function f(x) has an IZAR when f(a+bi) = a*g(bi) where the
      function g(x) strictly cannot be written as g(a+bi). I believe that
      if this condition has been met that the range of the function f(x)
      must have an ideal zero asymmetrical range about the value 'a' on its
      complex graph.

      He said... Tell me what you find most difficult or confusing about it.

      I wrote:

      It is my belief that Riemann saw this condition but wasn't able to
      define it, because the zeta function had gained so much popularity
      with its connection to prime numbers. I want to believe that my de-
      finition could be as fundamental for complex numbers as are the real
      number definitions for monoids, groups, rings, etc. in mathematics.

      He said... show me your work...

      I replied...

      After evaluating the zeta function for z(1/2+it), we get...

      2 4
      ------- + ------------- + ...
      (1+2it) (1-4t^2 +4it)

      and 1/2 * g(it) is the only way to factor out 1/2 from f(1/2+it) so
      by definition the ideal zero asymmetrical range must exist. It's my
      belief that several manipulations of the zeta function have been made
      in an effort to solve the problem and that definitions similar to the
      zero domain for real functions, etc. haven't been explored in the
      sense of the range of complex functions. It's been overlooked.

      I'm waiting for Dr. Rob's stimulating conversation... I won't be
      writing for a while... math is not my idea of fun... just under-
      standing. Bill Semper paratus.
    • leavemsg1
      ... ponder- ... the ... ...omit the restriction. The function should have been f(1/a + bi) = a * g(1+abi) ... it. ... de- ... real ... my ... made ... the ...
      Message 2 of 2 , Sep 6, 2006
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        --- In primenumbers@yahoogroups.com, "leavemsg1" <leavemsg1@...>
        wrote:
        >
        > I wrote to Dr. Math on 9/6/06... today.
        >
        > He asked... What is your question?
        >
        > I wrote:
        >
        > I see the many definitions that math books are filled with and
        ponder-
        > ed one myself. I call it the ideal zero asymmetrical range of a
        > complex function. It happens only when the following condition is
        > met. The function f(x) has an IZAR when f(a+bi) = a*g(bi) where
        the
        > function g(x) strictly cannot be written as g(a+bi).

        ...omit the restriction.

        The function should have been f(1/a + bi) = a * g(1+abi)


        > I believe that
        > if this condition has been met that the range of the function f(x)
        > must have an ideal zero asymmetrical range about the value 'a' on


        ...and the value of asymmetrical interest should have been '1/a'


        > its complex graph.
        >
        > He said... Tell me what you find most difficult or confusing about
        it.
        >
        > I wrote:
        >
        > It is my belief that Riemann saw this condition but wasn't able to
        > define it, because the zeta function had gained so much popularity
        > with its connection to prime numbers. I want to believe that my
        de-
        > finition could be as fundamental for complex numbers as are the
        real
        > number definitions for monoids, groups, rings, etc. in mathematics.
        >
        > He said... show me your work...
        >
        > I replied...
        >
        > After evaluating the zeta function for z(1/2+it), we get...
        >
        > 2))))))))))))))4
        > ------- + ------------- + ...
        > (1+2it) (1 + 2it)^2

        ... I changed this series to agree with the above changes ...

        >
        > and 2 * g(1+2it) is the only way to factor out 2 from f(1/2+it) so

        ... this was also corrected to yield more clarity ...

        > by definition the ideal zero asymmetrical range must exist. It's
        my
        > belief that several manipulations of the zeta function have been
        made
        > in an effort to solve the problem and that definitions similar to
        the
        > zero domain for real functions, etc. haven't been explored in the
        > sense of the range of complex functions. It's been overlooked.
        >
        > I'm waiting for Dr. Rob's stimulating conversation... I won't be
        > writing for a while... math is not my idea of fun... just under-
        > standing. Bill Semper paratus.
        >

        I haven't heard from Dr. Rob and think that he will either find the
        corrections to my original letter or skip the question entirely.

        Bill finally I clarified it for those in the group and myself
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