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Results tagged with analytic-number-theory
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user 475511
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.
3
votes
0
answers
128
views
Laplace transform of power of zeta function
Let $s$ is the complex variable. I would like to figure out the region of absolutely convergency of the following integral
$$
e^{\frac{is}{2}}\int\limits_{\frac{1}{2}-i\infty}^{\frac{1}{2}+i\infty}\G …
- 51
2
votes
1
answer
640
views
Mellin transform of powers of gamma function
If $a>0$, the Cahen-Mellin integral gives
$$\DeclareMathOperator{\Res}{\operatorname{Res}}
\frac{1}{2\pi i}\int\limits_{a-i\infty}^{a+i \infty}\varGamma(z) u^{-z}dz=e^{-u}=\sum\limits_{m=0}^{\infty}\ …
- 51