Analytic Proof of the Prime Number Theorem

Taking down $\psi(x)$ by complex integration

25 Mar 2021 Link

The Prime Number Theorem and Its Equivalences

Demystifying the counting function $\pi(x)$

24 Mar 2021 Link

Borel-Caratheodory Lemma and Its Application

Tactical estimation of logarithmic derivatives

16 Feb 2021 Link

Riemann-von Mangoldt formula for $\zeta(s)$

A powerful tool for us to study nontrivial zeros of $\zeta(s)$

19 Jan 2021 Link

Alternative Approach to Redefine $\zeta(s)$

Functional equation but the hardcore approach

05 Jan 2021 Link

Bernoulli Numbers and Their Associated Polynomials

One of the most brilliant tools in asymptotic analysis!

26 Dec 2020 Link

Mertens' Formula

A brilliant association between primes and logarithms

24 Dec 2020 Link

A Complete Investigation on Fourier Transform

A comprehensive derivation of different forms of Fourier transform

23 Dec 2020 Link

Jensen's Formula and Its Implications

Does maximum modulus tells distribution of roots?

14 Dec 2020 Link

Stirling's Formula

An efficient way to calculate factorial?

10 Dec 2020 Link

Analytic Continuation of the Riemann Zeta Function

Finally, we can catch a glimpse of the million-dollar math puzzle.

28 Nov 2020 Link

Factorial, Gamma Function, and More

One of the most commonly used way to implement factorials for complex numbers

13 Nov 2020 Link

Riemann-Stieltjes Integration and Asymptotics

Summation, but calculus approach

02 Nov 2020 Link

Möbius Inversion and Beyond

Arithmetic functions are fun!

14 Oct 2020 Link

Use Pycharm to Emulate Vim

What will you do if you don't know what vim is?

23 Jan 2018 Link

How to Create a Flashing Desktop

For those people who wanna make tricks

21 Jan 2018 Link

Welcome to my new website

Hello world

20 Jan 2018 Link