Appendix C

**Zeta-exponential function**

** **

As we know the
exponential function is:

_{}

The Riemann Zeta function is:

_{}

Combine the
exponential function and zeta function, and then we can have a new function,
which we temporally called the zeta-exponential function as follows:

_{}

Then we will get:

_{}

Thus:

_{}

Thus:

_{}

Thus:

_{}

Thus, we have:

_{}

The above equation is the Fourier
serial of the complex zeta-exponential function.

_{}

_{}

As we know:

_{}

Thus:

_{}

As we know for
the exponential function, we have:

_{}

_{}

_{}

Similar to the exponential
function, the complex zeta-exponential function has the following relationship:

_{}

_{}

_{}

_{}

for m =1 and _{}, thus we have

** **

_{}

** **

for m =1 and _{}, thus we have

** **

_{}

** **

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is the electron spin?
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