# All Questions

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### Does smooth section of a quotient space $G/H$ define an immersion?

Question 1: Let $G$ be a Lie group and $H<G$ a Lie subgroup of $G$, given the projection $p:G\to G/H$ and a smooth (local) section $s:G/H\to G$ s.t. $p\circ s=id$, then does this imply that $s$ is ...
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### Confused between multiple representations of Fourier Series' formula

I have never used the formula for Fourier Series with the representation that the instructor of the above video is using that involves $k$ and $\omega$. Instead, I use $n$ and $\pi$. Now, suppose ...
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### How to compute $\int_{\mathbb{C}} \frac{|dz|^2}{|z-a_1| \cdot |z-a_2| \cdot |z-a_3|}$ explicitly?

I have these integrals : $$I_1= \int_{\mathbb{C}} \frac{|dz|^2}{|z-a_1| \cdot |z-a_2| \cdot |z-a_3|},$$ and $$I_2= \int_{\mathbb{C}} \frac{|dz|^2}{|z-a_1| \cdot |z-a_2| \cdot |z-a_3| \cdot |z-a_4|}.$$ ...
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### Proof of the statement “The product of 4 consecutive integers can be expressed in the form 8k for some integer k”

I am slowly diving into simple number theory and learning how to craft direct proofs. I needed to proof the statement "The product of 4 consecutive integers can be expressed in the form 8k for some ...