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Results tagged with cv.complex-variables
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user 110710
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
1
vote
Integrate Faddeeva function
For the Faddeeva function
$$F(z)=e^{-z^2}\, \text{erfc}(-i z)\tag{1}$$
the integral
$$I=\int\limits_{-\infty}^{\infty} |F(z)|^2 \, dz\tag{2}$$
can be evaluated using the Plancherel theorem
$$\int\limi …
- 1,126
1
vote
When is $\Re(\zeta(s)) - \Im(\zeta(s)) = 0 $ with $\Re(\zeta(s))\neq 0$ and $\Im(\zeta(s))\n...
Here are a couple of contour plots of
$$\Re(\zeta(\alpha+i \beta))=\Im(\zeta(\alpha+i \beta))\quad\tag{blue curve}$$
$$\Re(\zeta(\alpha+i \beta))=0\quad\tag{orange curve}$$
$$\Im(\zeta(\alpha+i \beta) …
- 1,126