New function

Chinmay has had the idea of a function for some time, today we were able to get some stuff off of it.

we define (Chinmay's definition): $Ch(n)=\begin{cases} 1&, n=\text{ prime} \\ (-1)^{\tau(n)}&,\text{ otherwise}\end{cases}$ Later, I made it to $Ch(n)=\begin{cases} -1&, n=\text{perfect square}\\ 1&,\text{otherwise}\end{cases}$ this is trivial, (tau is odd iff $n$ is a perfect square, tau of all primes are 2). let's find its Dirichlet series $D(Ch;s)=-2\zeta(2s)+\zeta(s)$ This is an interesting result, we will try to apply it in future notes.

#Calculus

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$