Week6Lecture5: The Prime Number Theorem

[bmz]

Thank you very much for these lectures. You are definitely the Explainer-in-Chief. So easy to understand you.

[NoSpaceAwareness]

Thank you so much for making this course. I'm using it to prepare for university, but I've found so much more from it than I could have expected, and it's only made me more curious and excited about what maths has to offer!

[drumetul_dacic]

Thank you very much for publishing this great videos. I find it very easy to watch and understand the way you explain. You're a very good teacher. I wish I had a math teacher like you while I was in school. Thanks again and keep up the good work :)

[utsee]

Dr. Petra, thank you for the BEST explanation of the relationship between prime # theorem, zeta fx, and Riemann hypothesis. I say that after intensive research on this topic over the last 18 mos, ..new follower. Will teach it to my students this way from now on. My compliments.

[twistedlot]

Well done. I thoroughly enjoyed this course on complex analysis. I give the professor an A+

[mb]

Very good Petra, gives a good insight to the PNT for the interested beginner.

[季明強]

I like your explanation of these two lectures on the trivial zero of zeta function

[jannis]

I love those videos way better than school

[Dogzz]

Of course, I enjoyed the course. Thank you so much!

[ffhashimi]

This Great and very useful; Thanks a lot .

[tariqrashid]

At 10:30 is it stated that the infinite product can't be zero because none of the factors are zero. However, infinite products like 1/2*1/3*1/4*1/5*... tend to zero while none of the factors are zero. Another example is ∏(1-1/n), with n starting at 2, tends to zero but none of the factors (1-1/n) are zero. How can we still say the product form of the 𝛇(s) therefore has no zeros for 𝜎>1 ?

[lokeshkumar]

Why (1+....) This term is coming in your . It is wrong

[ritamchakraborty]

the best channel on this field but expected atleast the mention of the name Ramanujan as you are dealing with prime numbers

[Kybeline]

Do I understand it right? Is there no real nummerical proof of the relation between zeta function and the prime distribution? Only analytic proof by the behaviour of those functions? I mean, one cannot explain the distribution-rate of the primes without using logarithmic or integral logarithmic formulas?

[sergiofernandez]

You can write an equation to count an get an exact value not an approximation.

[magicfigures]

The new finds in the field of prime numbers. The prime numbers form so-called nests of the prime numbers in the fourth dimensions. Please see the homepage www.number-galaxy.eu in the directory "news" and positions:
01.01.2020 3D bordered prime magic squares in world and antiworld configuration
03.02.2021 Projection 3D bordered prime magic squares on critical linie of Riemann zeta-function.
This is completely new in the field of the Riemann hypothesis.

[MrBorceivanovski]

I have a proof of the Riemann hypothesis #&#

[KafrosKypselis]

No proof given. Just a vague historical description of the sequence of steps needed for the proof. You HAVE to read Riemann's paper, it might take you a month or two but it's worth it.