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On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.

14 votes

Why does the Gamma-function complete the Riemann Zeta function?

"Why of all functions does one have to put the Gamma-function there?" $\zeta(s)$ has trivial zeroes at $-2, -4, -6$, etc. $\zeta(1-s)$ thus has trivial zeroes at $s=3, 5, 7$, etc - a completely diffe …
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