1.RMIT - SAMVAAD TALK00:00
2.COVID-1901:46
3.The Dirichlet Divisor Problem02:00
4.Quote from Ramanujan's First Letter to Hardy03:01
5.Quote from Hardy03:51
6.G. H. Hardy05:06
7.Quote from Watson05:10
8.Page 307 in Ramanujan's Second Notebook05:45
9.Page 350 in Ramanujan's Second Notebook06:19
10.Appearances in Ramanujan's Notebooks06:50
11.Circle Problem08:54
12.The Circle Problem10:18
13.Sierpinski's Theorem and Huxley's Theorem14:48
14.Another Beautiful Identity of Ramanujan as Recorded by
Hardy16:20
15.Explanation of Notation18:20
16.An Elementary Formula19:59
17.First Identity21:07
18.Page 335 in Ramanujan's Lost Notebook21:45
19.Ramanujan's First Claim21:57
20.The First Entry22:08
21.Version of BCB & Zaharescu22:34
22.Remarks22:40
23.Another Result from Ramanujan's First Letter to Hardy25:01
24.Dirichlet divisor problem26:13
25.Geometric Interpretation26:54
26.Geometrical Interpretation27:42
27.Dirichlet's Argument28:22
28.Voronoi's Formula30:40
29.Voronoi's Bound for A(x)31:22
30.Second Identity32:00
31.Ramanujan's Second Identity32:09
32.Remarks32:30
33.The Final Problem33:55
34.Final Problem for George Andrews and Myself35:34
35.What Happened36:12
36.Junxian Li and Alexandr Zaharescu37:10
37.Sketch of the Proof37:18
38.Sketch of the Proof, Continued39:03
39.Are these Two Formulas of Ramanujan Isolated?39:35
40.An Analogue of Ramanujan's identity for 13(n)39:54
41.Trigonometric Sums40:36
42.Trigonometric Sums, Cont.42:32
43.Conjecture for SS(o, 0; x)43:30
44.Theorem for SS(o, 0; x)44:07
45.Special Case: A Lattice Point Problem45:14
46.Multivariable sin Sum46:58
47.References47:10
48.Martino Fassina47:52
49.Alexandr Zaharescu48:10
50.General Setting: Chandrasekaran and Narasimhan48:20
51.General Setting: Chandrasekaran and Narasimhan,
continued49:13
52.(n)51:41
53.Example: Ramanujan's Arithmetical Function an = T(n)52:01
54.Reference52:59
55.Another Final Problem53:12
56.Brief Introduction to Ramanujan's Theta Functions53:39
57.Values of 4(q)55:13
58.Value of 4(e-13T56:15
59.An Unsolved Problem57:10
60.Stay Tuned57:41
61.Questions; Problems58:19
62.Appreciation59:29