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The Fundamental Theorem of Probabilistic Number Theory - Shared screen with speaker view
espen slettnes
04:02
Handout: https://espen.slett.net/BMC_lectures/Probabilistic_Number_Theory/2020-06-17.pdf
Jake Robb
10:55
yes
Derek Liu
10:55
yes
Sebastian Weinberger
10:59
yes
Sheldon Tan
11:00
yes
Andrew Sylvester
12:38
3
Sebastian Weinberger
12:39
3
Jake Robb
12:41
3
Derek Liu
12:53
403?
Derek Liu
12:55
aw
Derek Liu
12:56
2
Nathan Barnes
12:57
2
Sheldon Tan
12:57
2
Zihongbo Wang
12:57
2
Owen Xu
12:58
2
Andrew Sylvester
12:59
2
Jewoo Suh
13:01
2
Sebastian Weinberger
13:02
2
Derek Liu
13:06
0
Sheldon Tan
13:07
0
Owen Xu
13:08
0
Sebastian Weinberger
13:08
0
Derek Liu
13:22
is -v(o) infinity
Derek Liu
13:25
oops
Derek Liu
13:38
is 'v(0) is defined as infinity or undefined?
Sheldon Tan
13:51
idk maybe infinity
Derek Liu
14:18
what's omega again
Sheldon Tan
14:58
its some variable that goes to infinity i thing
Sheldon Tan
15:01
think
Sheldon Tan
16:32
lol does anyone follow this?\
Sheldon Tan
17:34
normal distribution?
Sebastian Weinberger
17:53
Markov?
Andrew Sylvester
18:02
markovs inequality
Sebastian Weinberger
18:25
Oh wait I mean Chebyshev’s inequality
Derek Liu
19:00
what does omega(n|sqrt(lnlnn)) mean again
Sheldon Tan
19:56
ok
Derek Liu
19:59
whats omega(n) again
Derek Liu
20:02
I cant remember
Jake Robb
21:30
I ready to move on
Derek Liu
21:32
i don't think we have questions
Sebastian Weinberger
21:36
I’m ready
Eddy Li
21:38
what's omega
Sheldon Tan
21:54
any function that goes to infinity at any rate
Eddy Li
21:57
ok
Sheldon Tan
23:03
so just pi of d?
Derek Liu
23:40
n-D?
Sheldon Tan
23:50
of m
Derek Liu
23:51
though this is a horrible bound
Sheldon Tan
23:52
oh
Sheldon Tan
24:07
lol
Nathan Barnes
24:11
v(m)
Derek Liu
24:20
136?
Derek Liu
24:38
because we cannot have 137 prime factors above 137th root of n
Derek Liu
24:43
or they would multiply to more than n
Sheldon Tan
26:57
just wondering how do you spell the function for v
Sheldon Tan
27:01
"new"
Eddy Li
28:40
in X_p, is m random?
Jake Robb
29:02
v(m)
Derek Liu
30:06
1/p
Derek Liu
30:25
floor(n/p)/n?
Derek Liu
31:32
O(1)?
Derek Liu
32:27
ln D /n?
Derek Liu
32:35
oops
Derek Liu
33:52
1/137 ln ln n
Derek Liu
33:54
wait
Derek Liu
33:55
no
Nathan Barnes
33:55
ln(ln(n))-O(1)
Derek Liu
34:02
ln (1/137 ln n)
Leo Xu
34:07
^
Sebastian Weinberger
34:23
= ln(1/137)+ln(ln(n))
Derek Liu
35:54
do variances like "add in quadrature" or something
Derek Liu
39:18
Cov=E[X]E[Y]-E[XY]
Derek Liu
39:24
i think i got it opposite
Derek Liu
39:26
negative that
Derek Liu
40:44
1/p
Derek Liu
41:28
its around 1/p+1/q-1/pq
Derek Liu
41:33
but replace 1/p with floor(n/p)/n
Nathan Barnes
41:35
E[X_p]E[X_q}
Derek Liu
41:36
wiat oops
Derek Liu
41:40
im trolling
Derek Liu
44:13
because we've shown this before
Derek Liu
44:59
1/pn+1/qn-1/n^2
Andrew Sylvester
45:50
q-p times?
Nathan Barnes
45:56
O(n/log(n))
Nathan Barnes
46:09
I mean D
Derek Liu
46:09
together it should be like v'(n)?
Derek Liu
46:17
or twice that
Nathan Barnes
47:35
n^(136/137)
Jake Robb
47:35
the power term
Derek Liu
49:34
ceiling of ln ln n
Derek Liu
50:15
normal distributions?
Derek Liu
54:16
product of all 1/p?
Nathan Barnes
54:21
n/log(n)
Nathan Barnes
54:35
O(π(D))
Derek Liu
55:12
137/
espen slettnes
57:38
Homework: hw29, not hw33, bhw 34 but for hardy Ramanujan
espen slettnes
59:17
Bhw: prove p|(2n choose n) combinatorially
Derek Liu
01:02:19
Thank you!
Sebastian Weinberger
01:02:27
Thank you!
Leo Xu
01:02:28
Thank you!
Golden Peng
01:02:30
Thanks!
Jake Robb
01:02:31
Thanks Espen! That was a fun class.
Andrew Sylvester
01:02:34
Thanks for class!
Zihongbo Wang
01:02:40
Thanks
Sheldon Tan
01:02:42
Thank you!
Jewoo Suh
01:02:44
Thank you!
Owen Xu
01:02:45
thank you!
Sebastian Weinberger
01:02:49
Thank you! This was so fun!
Andrew Park
01:02:50
thank you
Teresa Marin
01:02:58
Thanks