## hopefully knowing the zeta function

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• ... 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 1 of 2 , Sep 6, 2006
wrote:
>
> I wrote to Dr. Math on 9/6/06... today.
>
>
> 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
> 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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