Questions tagged [complex-analysis]

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When did people know that all real polynomials of degree greater than 2 are reducible?

Admittedly, this may not be a research level question, but I am deeply curious about this. Let $f(x) \in \mathbb{R}[x]$, and write $d = \deg f$. It is well known that if $\deg f > 2$, then $f$ is ...
4
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0answers
79 views

Variants in graphical presentation of real and complex numbers

It's standard nowadays for the real line to be horizontal (negative numbers on the left, positive numbers on the right) and for $i$ to be above (rather than below) 0 in the complex plane. Were these ...
3
votes
0answers
65 views

How much ground was prepared for Riemann so that he could conjecture Riemann hypothesis?

Although I do not doubt in Riemann˙s originality, I would like to know how much complex analysis was developed up to the day when Riemann conjectured what is today called Riemann hypothesis and how ...
3
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0answers
66 views

Analytic and holomorphic functions, definitions and foundations?

If you search for the definition of analytic and holomorphic functions in books and online, you get crosses between two definitions (one involving taylor series and one differential) I can find no ...
1
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136 views

$[\operatorname{Cos}(x)+i\operatorname{Sin}(x)]\cdot[\operatorname{Cos}(y)+i\operatorname{Sin}(y)]=\operatorname{Cos}(x+y)+i\operatorname{Sin}(x+y)$

Had this non-analytic theorem ever been known before Euler discovered his analytic formula: $\operatorname{Cos}(x)+i\operatorname{Sin}(x)= e^{ix}$ ? Please notice the distinction between, the theorem ...
1
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58 views

gauss' opinion on de moivre's theorem

What did Gauss mean when he said that you'd never be a good mathematician if you didn't think that De Moivre's theorem was obvious? I'm looking for a specifically historically correct answer with ...
0
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0answers
74 views

How did Hardy and Littlewood formulate the k-tuple conjecture?

Let $\mathcal{H}_k = (h_1,h_2,\cdots,h_k)$ be an admissible k-tuple. The k-tuple conjecture predicts that the number of primes $(b+h_1,b+h_2,\cdots,b+h_k)\in \mathbb{P}^k$ with $b+h_k \leq x$ is: $$\...