Gaussian Numbers

sven-h.simon sven-h.simon at
Sun Jan 16 10:29:41 CET 2005

I would appreciate clear definitions for functions like Sigma and so on in the 
complex plane too.
In the discussions, an article of Spira was mentionend, which I ordered at once.

I think complex numbers are an important mathematical component (Fourier 
Transforms, Riemann ... ) and I am little bit surprised about the lack of 
definitions, knowledge and research here. On the other hand the currently 
discussed themes are mainly math fun.

Complex numbers are a complex theme, so I do not think, I should do research 
work in the fundamental concepts here. 

One question I have in this context: I contributed several sequence about counts 
of complex primes. These primes were ordered by their norm (was sometimes called 
abs here, I think). I counted 1+i as the first complex prime, and continued with 
primes corresponding to the primes 1 mod 4 . 
The next one is 1 + 2i (with 5 as corresponding prime). Is it common sense to 
count 1+i as the first complex prime ?

Complex primes for me are primes in the complex plane, that have both real and 
imaginary parts as natural integers greater than 0. The other primes 3 mod 4 
appear only on the axis of the complex plane, having real or imaginary part 0.
The imaginary part is just the prime itself multiplicated with the unit i.

Of course it would not bother me, if my definition is not common sense ..., I 
just would like to know. For me starting with 1+i in the sequence of 'complex 
primes' as defined above is not completly wrong. 

Sven Simon

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