this series is so exciting! when I first saw the course, I don't know the author is a fields medal winner,I just feel that he explained so clearly about the p-adic number theory. then I got to know his identity from the comment, wonderful!
guys, stop pointing out little typos in the lectures as if they were errors. These lectures are amazing and clearly Dr. Borcherds is putting so much effort into them, the lectures are recorded "live" and handwritten, which I love, because they have so much more life in them. If you want lectures with no typos read a textbook. I love these lectures and love the typos, because these lectures feel very personal and bring so much life to maths,
I'm absolutely amazed at how Number theorists have managed to ascribe a complete vector space to the methods of factorization. When I first saw this correlation presented in Shimura I was totally bewildered, but its an incredible concept that I feel is underrepresented in its applications to the sciences. It seems particularly well suited to modelling of entropy and the nuances of ergodic systems with nonlinear principles of motion. Physicists really shouldve stayed in school if you can pardon the pun 😂
this series is so exciting! when I first saw the course, I don't know the author is a fields medal winner,I just feel that he explained so clearly about the p-adic number theory. then I got to know his identity from the comment, wonderful!
11:36 “so we notice that 1 is less than infinity”
No way
I can prove it if you like:
1. 0 < 1
2. 1 * 0 < 1 * 1
3. 1 * 0 / 0 < 1 / 0
4. 1 * 1 < infinity
5. 1 < infinity
In p-adic integers "infinity" is less then 1 lol
guys, stop pointing out little typos in the lectures as if they were errors. These lectures are amazing and clearly Dr. Borcherds is putting so much effort into them, the lectures are recorded "live" and handwritten, which I love, because they have so much more life in them. If you want lectures with no typos read a textbook. I love these lectures and love the typos, because these lectures feel very personal and bring so much life to maths,
I'm absolutely amazed at how Number theorists have managed to ascribe a complete vector space to the methods of factorization. When I first saw this correlation presented in Shimura I was totally bewildered, but its an incredible concept that I feel is underrepresented in its applications to the sciences. It seems particularly well suited to modelling of entropy and the nuances of ergodic systems with nonlinear principles of motion. Physicists really shouldve stayed in school if you can pardon the pun 😂
That was awesome proof and very easy to understand thanks a lot
Would you make a lecture on partition of integers ?
00:47 Should it be χ(n)=0 when (n,N)≠1?
No, what he wrote is correct.
For example, working mod 5, chi_0 goes 1,1,1,1,0,1,1,1,1,0,1,1,1,1,0, ...
Edit: Thomas is right
@@malharmanagoli the sequence you described is 0 when (n,N)=5 and not 1, so it's 0 when (n,N)≠1, just as Thomas said.
@@diribigal My bad. You're right
It's like the third lecture in a row where that mistake pops up
Nice lecture, very helpful
Thanks
What do you thing about Reiman hypothesis?
yeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee