I only recently discovered your channel and am very glad to have it! Having worked my way through the Erdos "elementary" proof of the PNT (twice!!), I was impressed with how much value you were able to pack into your video. Thank you for providing such essential content!!
Dude, I must seriously thank you because I am writing a paper on prime numbers but I couldn't understand some key terms in PNT such as the Chebyshev functions however you explained everything in a concise and understandable way. I really like how you present math in a clean way and how you get straight to the point. I look forward to watching your other videos. Well Done for such a wonderful video! I hope you get more subscribers in the future
Unfortunately, this is a massively under-appreceated channel! I just hope you don't stop producing such an exquisite content due to (yet) few subscribers :( Keep it up!!!
Thanks for the very kind words. I have quite a lot of views (about 1 million) but not many subscribers. I think this is because a lot of my videos help university students with course work and new videos of mine will rarely appear at a time to help them with their new topics. Again, many thanks.
Manal Saad Try Theorem 13.2 from Introduction to Analytic Number Theory by Tom M. Apostol, which is, by the way, an excellent book for those interested in number theory.
Hi Shuoyan, in my opinion the best books for you would be An introduction to the theory of numbers by Hardy and Wright or Introduction to Analytic Number Theory by Tom Apostol. Good luck.
Me: Proof PNT to me please. Randell: Here's some formul- Me after reqognizing the formulas from a video on the Riemann Hypothesis: Hold on! I like to challenge myself, but I'm not a masochist.
One of my colleagues, Peter Brown, has a playlist that covers the theorem. Search his playlist, journey into number theory, and you should be able to find it. Otherwise just search proof prime number theorem on Google and find a proof that uses the sort of ideas that are on my video.
I only recently discovered your
channel and am very glad to
have it! Having worked my way
through the Erdos "elementary"
proof of the PNT (twice!!), I was
impressed with how much value
you were able to pack into your
video. Thank you for providing
such essential content!!
Thanks for taking the time to comment.
Dude, I must seriously thank you because I am writing a paper on prime numbers but I couldn't understand some key terms in PNT such as the Chebyshev functions however you explained everything in a concise and understandable way. I really like how you present math in a clean way and how you get straight to the point. I look forward to watching your other videos. Well Done for such a wonderful video! I hope you get more subscribers in the future
ken chang Thanks Ken. Glad it helped.
+Randell Heyman I did not understand what happened at 11:50 , How did π (2) and the other numbers become
π (t)?
@@kentucky3692 can you please teach me prime number theorem?
Unfortunately, this is a massively under-appreceated channel! I just hope you don't stop producing such an exquisite content due to (yet) few subscribers :( Keep it up!!!
Thanks for the very kind words. I have quite a lot of views (about 1 million) but not many subscribers. I think this is because a lot of my videos help university students with course work and new videos of mine will rarely appear at a time to help them with their new topics. Again, many thanks.
Great video and proof! Is there a proof (anywhere) that shows psi 1 of x is equal to that really long integral?
Manal Saad Try Theorem 13.2 from Introduction to Analytic Number Theory by Tom M. Apostol, which is, by the way, an excellent book for those interested in number theory.
Thanks so much, do you also have any rrcommended reference for further details? cheers :D
Hi Shuoyan, in my opinion the best books for you would be An introduction to the theory of numbers by Hardy and Wright or Introduction to Analytic Number Theory by Tom Apostol. Good luck.
Me: Proof PNT to me please.
Randell: Here's some formul-
Me after reqognizing the formulas from a video on the Riemann Hypothesis: Hold on! I like to challenge myself, but I'm not a masochist.
this paper helps me a lot in writing my paper on the survey of prime number theorem
It would be good to see your survey when finished. If you are happy for me to see it email me through my website.
Can I find proof from the end of the video published anywhere? It seems not so rigorous for that difficult problem
One of my colleagues, Peter Brown, has a playlist that covers the theorem. Search his playlist, journey into number theory, and you should be able to find it. Otherwise just search proof prime number theorem on Google and find a proof that uses the sort of ideas that are on my video.
Did you get it?
Where can find the proof for the integral part at the end?
+King Munch Introduction to Analytic Number Theory by Tom M Apostol, Theorem 4.4
Randell Heyman thank you.
@@kingmunch7252 please can you teach me prime number theorem?