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Results tagged with cv.complex-variables
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user 37555
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
1
vote
Estimating the height required to find a given small value of $|\zeta(s)|$ near the line $\s...
It suffices to construct points in the rectangle with $|\zeta(s)|\leq\delta$. This can be done, even to the right of 1, by diophantine approximation: Pick some $t$, such that for the first $k$ primes …
8
votes
meromorphic extension of dirichlet series
The maximal domain of meromorphic continuation of a Dirichlet series can be anything.
More precisely, for every connected open subset $O$ of $\mathbb{C}$, which contains the half plane $\{\Re s>1\}$, …
5
votes
Demystifying complex numbers
From the point of view of enginieers, the most obvious application of complex numbers is computing alternating currents.
Consider first direct current. If you have a network of resistors, and want to …
6
votes
What is the relationship between the abscissa of holomorphy and abscissa of convergence of a...
In general the answer is no, but if you assume that the $a_n$ are non-negative, then Landau's theorem tells you that $\phi$ has a singularity at $\sigma_{\mathrm{conv}}$, in particular $\sigma_{\mathr …
1
vote
Special values of $\zeta$ outside the real line and the critical strip
There is a well known conjecture that the ordinates of the non-trivial zeros of $\zeta$ are $\mathbb{Q}$-linearly independent.
There are two major motivations for this conjecture. First all numbers …