| # |
Date |
Duration |
Folks |
Topic |
| 1 |
Fri, 05 Mar 2021 15:30 UTC |
40 mins |
4 |
Introduction to Analytic Number Theory: Sections 1.1-1.3: Pages 13-16: Principle of Induction; Divisibility |
| 2 |
Sat, 06 Mar 2021 10:00 UTC |
40 mins |
5 |
Introduction to Analytic Number Theory: Section 1.1: Page 13: Principle of induction (Recap) |
| 3 |
Sun, 07 Mar 2021 10:00 UTC |
40 mins |
5 |
Introduction to Analytic Number Theory: Sections 1.2: Page 14: Divisibility (Recap) |
| 4 |
Mon, 08 Mar 2021 18:00 UTC |
40 mins |
6 |
Introduction to Analytic Number Theory: Sections 1.2-1.3: Pages 14-16: Divisibility, GCD |
| 5 |
Tue, 09 Mar 2021 18:00 UTC |
40 mins |
10 |
Introduction to Analytic Number Theory: Sections 1.4-1.5: Pages 16-18: Prime numbers, Fundamental theorem of arithmetic |
| 6 |
Wed, 10 Mar 2021 18:00 UTC |
40 mins |
10 |
Introduction to Analytic Number Theory: Section 1.6: Pages 18-19: The series of reciprocals of primes |
| 7 |
Thu, 11 Mar 2021 18:00 UTC |
40 mins |
11 |
Introduction to Analytic Number Theory: Sections 1.7-1.8: Pages 19-21: The Euclidean algorithm, GCD of more than two numbers |
| 8 |
Fri, 12 Mar 2021 18:00 UTC |
40 mins |
9 |
Introduction to Analytic Number Theory: Sections 2.1-2.2: Pages 24-25: The Möbius function \( \mu(n) \) |
| 9 |
Sun, 14 Mar 2021 09:00 UTC |
40 mins |
5 |
Introduction to Analytic Number Theory: Sections 2.1-2.2: Pages 24-25 (Recap) |
| 10 |
Mon, 15 Mar 2021 18:00 UTC |
40 mins |
12 |
Introduction to Analytic Number Theory: Sections 2.3-2.4: Pages 25-27: The Euler totient function \( \varphi(n), \) A relation connecting \( \varphi \) and \( \mu \) |
| 11 |
Tue, 16 Mar 2021 18:00 UTC |
40 mins |
14 |
Introduction to Analytic Number Theory: Sections 2.5-2.6: Pages 27-30: A product formula for \( \varphi(n), \) The Dirichlet product of arithmetical functions |
| 12 |
Wed, 17 Mar 2021 18:00 UTC |
40 mins |
12 |
Introduction to Analytic Number Theory: Sections 2.7-2.8: Pages 20-33: Dirichlet inverses and the Möbius inversion formula, The Mangoldt function \( \Lambda(n) \) |
| 13 |
Thu, 18 Mar 2021 18:00 UTC |
40 mins |
10 |
Introduction to Analytic Number Theory: Section 2.7-2.8: Pages 20-33 (Recap) |
| 14 |
Fri, 19 Mar 2021 18:00 UTC |
40 mins |
9 |
Introduction to Analytic Number Theory: Sections 2.9-2.10: Pages 33-36: Multiplicative functions, Multiplicative functions and Dirichlet multiplication |
| 15 |
Mon, 22 Mar 2021 18:00 UTC |
40 mins |
10 |
Introduction to Analytic Number Theory: Sections 2.11-2.13: Pages 36-39: The inverse of a completely multiplicative function, Lioville's function \( \lambda(n), \) The divisor functions \( \sigma_{\alpha}(n) \) |
| 16 |
Tue, 23 Mar 2021 18:00 UTC |
40 mins |
12 |
Introduction to Analytic Number Theory: Section 2.14: Pages 39-40: Generalized convolutions |
| 17 |
Wed, 24 Mar 2021 18:00 UTC |
30 mins |
11 |
Introduction to Analytic Number Theory: Section 2.15: Pages 41-42: Formal power series |
| 18 |
Thu, 25 Mar 2021 18:00 UTC |
40 mins |
10 |
Introduction to Analytic Number Theory: Sections 2.16-2.17: Pages 42-45: The Bell series of an arithmetical function, Bell series and Dirichlet multiplication |
| 19 |
Fri, 26 Mar 2021 18:00 UTC |
40 mins |
10 |
Introduction to Analytic Number Theory: Sections 2.18-2.19: Pages 44-46: Derivatives of arithmetical functions, The Selberg identity |
| 20 |
Mon, 29 Mar 2021 18:00 UTC |
40 mins |
11 |
Introduction to Analytic Number Theory: Sections 3.1-3.3: Pages 52-55: The big oh notation, Euler's summation formula |
| 21 |
Tue, 30 Mar 2021 18:00 UTC |
40 mins |
12 |
Introduction to Analytic Number Theory: Section 3.4: Pages 55-57: Some elementary asymptotic formulas |
| 22 |
Wed, 31 Mar 2021 18:00 UTC |
40 mins |
12 |
Introduction to Analytic Number Theory: Section 3.5: Pages 57-59: The average order of \( d(n) \) |
| 23 |
Fri, 02 Apr 2021 18:00 UTC |
40 mins |
12 |
Introduction to Analytic Number Theory: Section 3.6: Pages 60-61: The average order of the divisor functions \( \sigma_{\alpha}(n) \) |
| 24 |
Mon, 05 Apr 2021 18:00 UTC |
40 mins |
11 |
Introduction to Analytic Number Theory: Section 3.7: Pages 61-62: The average order of \( \varphi(n) \) |
| 25 |
Tue, 06 Apr 2021 18:00 UTC |
40 mins |
11 |
Introduction to Analytic Number Theory: Sections 3.8-3.10: Pages 62-65: An application to the distribution of lattice points visibile from the origin, The average order of \( \mu(n) \) and of \( \Lambda(n), \) The partial sums of a Dirichlet product |
| 26 |
Wed, 07 Apr 2021 18:00 UTC |
40 mins |
10 |
Introduction to Analytic Number Theory: Section 3.11: Pages 66-69: An application to the distribution of lattice points visibile from the origin, The average order of \( \mu(n) \) and of \( \Lambda(n), \) The partial sums of a Dirichlet product |
| 27 |
Fri, 09 Apr 2021 18:00 UTC |
30 mins |
9 |
Introduction to Analytic Number Theory: Section 3.12: Pages 69-70: Another identity for the partial sums of a Dirichlet product |
| 28 |
Mon, 12 Apr 2021 18:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Sections 4.1-4.2: Pages 74-76: Cheybyshev's functions \( \psi(x) \) and \( \vartheta(x) \) |
| 29 |
Mon, 12 Apr 2021 18:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Sections 4.1-4.2: Pages 74-76: Cheybyshev's functions \( \psi(x) \) and \( \vartheta(x) \) |
| 30 |
Tue, 20 Apr 2021 18:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 4.3: Pages 76-79: Relations connecting \( \vartheta(x) \) and \( \pi(x) \) (Abel's identity) |
| 31 |
Wed, 21 Apr 2021 18:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 4.4: Pages 79-80: Some equivalent forms of the prime number theorem (Theorem 4.4) |
| 32 |
Thu, 22 Apr 2021 18:00 UTC |
40 mins |
9 |
Introduction to Analytic Number Theory: Section 4.4: Pages 80-82: Some equivalent forms of the prime number theorem (Theorem 4.5) |
| 33 |
Mon, 26 Apr 2021 18:00 UTC |
40 mins |
9 |
Introduction to Analytic Number Theory: Section 4.5: Pages 82-84: Inequalities of \( \pi(n) \) and \( p_n \) (Theorem 4.6) |
| 34 |
Tue, 27 Apr 2021 18:00 UTC |
40 mins |
9 |
Introduction to Analytic Number Theory: Section 4.5: Pages 84-85: Inequalities of \( \pi(n) \) and \( p_n \) (Theorem 4.7) |
| 35 |
Wed, 28 Apr 2021 18:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Sections 4.6-4.7: Pages 85-89: Shapiro's Tauberian theorem |
| 36 |
Thu, 29 Apr 2021 18:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Section 4.8: Pages 89-91: An asymptotic formula for the partial sums \( \sum_{p \le x} (1/p) \) |
| 37 |
Fri, 30 Apr 2021 18:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Section 4.9: Pages 91-94: The partial sums of the Möbius function (Theorems 4.13-4.14) |
| 38 |
Mon, 03 May 2021 18:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 4.9: Pages 94-97: The partial sums of the Möbius function (Theorem 4.15) |
| 39 |
Wed, 05 May 2021 18:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 4.9: Pages 97-98: The partial sums of the Möbius function (Theorem 4.16) |
| 40 |
Thu, 06 May 2021 18:00 UTC |
40 mins |
5 |
Introduction to Analytic Number Theory: Sections 5.1-5.2: Pages 106-110: Definition and basic properties of congruences, Residue classes and complete residue systems |
| 41 |
Fri, 07 May 2021 18:00 UTC |
40 mins |
9 |
Introduction to Analytic Number Theory: Section 5.3: Pages 110-113: Linear congruences |
| 42 |
Tue, 11 May 2021 18:00 UTC |
40 mins |
10 |
Introduction to Analytic Number Theory: Section 5.4: Pages 113-114: Reduced residue systems and the Euler-Fermat theorem |
| 43 |
Wed, 12 May 2021 18:00 UTC |
40 mins |
10 |
Introduction to Analytic Number Theory: Sections 5.5-5.6: Pages 114-116: Polynomial congruences modulo \( p, \) Lagrange's theorem, Applications of Lagrange's theorem (Wilson's theorem) |
| 44 |
Thu, 13 May 2021 18:00 UTC |
40 mins |
11 |
Introduction to Analytic Number Theory: Sections 5.6-5.7: Pages 116-118: Wolstenholme's theorem, The Chinese remainder theorem |
| 45 |
Fri, 14 May 2021 18:00 UTC |
40 mins |
9 |
Introduction to Analytic Number Theory: Section 5.8: Pages 118-120: Applications of the Chinese remainder theorem |
| 46 |
Wed, 19 May 2021 18:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Section 5.9: Pages 120-122: Polynomial congruences with prime power moduli |
| 47 |
Thu, 20 May 2021 18:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Section 5.10: Pages 123-124: The principle of cross-classification (Theorem 5.31) |
| 48 |
Fri, 21 May 2021 18:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 5.10-5.11: Pages 124-126: The principle of cross-classification (Theorem 5.32), A decomposition property of reduced residue system |
| 49 |
Tue, 25 May 2021 18:00 UTC |
40 mins |
12 |
Introduction to Analytic Number Theory: Sections 6.1-6.3: Pages 129-131: Definitions, Examples of groups and subgroups, Elementary properties of groups |
| 50 |
Wed, 26 May 2021 18:00 UTC |
40 mins |
11 |
Introduction to Analytic Number Theory: Section 6.4: Pages 131-133: Construction of subgroups |
| 51 |
Thu, 27 May 2021 18:00 UTC |
40 mins |
12 |
Introduction to Analytic Number Theory: Sections 6.5-6.6: Pages 133-136: Characters of finite abelian groups, The character group |
| 52 |
Fri, 28 May 2021 18:00 UTC |
40 mins |
11 |
Introduction to Analytic Number Theory: Section 6.7: Pages 136-137: The orthogonality relations for characters |
| 53 |
Mon, 31 May 2021 18:00 UTC |
40 mins |
11 |
Introduction to Analytic Number Theory: Section 6.8: Pages 137-140: Dirichlet characters |
| 54 |
Tue, 01 Jun 2021 18:00 UTC |
40 mins |
9 |
Introduction to Analytic Number Theory: Section 6.9: Pages 140-141: Sums involving Dirichlet characters |
| 55 |
Wed, 02 Jun 2021 18:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 6.10: Pages 141-143: The nonvanishing of \( L(1, \chi) \) for real nonprincipal \( \chi \) |
| 56 |
Thu, 03 Jun 2021 18:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 7.1-7.2: Pages 146-147: Dirichlet's theorem for primes of the form \( 4n - 1 \) and \( 4n + 1 \) |
| 57 |
Fri, 04 Jun 2021 18:00 UTC |
30 mins |
7 |
Introduction to Analytic Number Theory: Sections 7.3-7.4: Pages 148-151: The plan of the proof of Dirichlet's theorem, Proof of Lemma 7.4 |
| 58 |
Mon, 07 Jun 2021 18:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 7.5: Pages 151-152: Proof of Lemma 7.5 |
| 59 |
Thu, 10 Jun 2021 18:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 7.6-7.9: Pages 152-155: Proof of Lemma 7.6, Proof of Lemma 7.8, Proof of Lemma 7.7, Distribution of primes in arithmetic progressions |
| 60 |
Tue, 15 Jun 2021 17:00 UTC |
40 mins |
9 |
Introduction to Analytic Number Theory: Sections 8.1-8.2: Pages 157-160: Functions periodic modulo \( k, \) Existence of finite Fourier series for periodic arithmetical functions |
| 61 |
Wed, 16 Jun 2021 17:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Section 8.3: Pages 160-162: Ramanujan's sum and generalizations |
| 62 |
Thu, 17 Jun 2021 17:00 UTC |
40 mins |
13 |
Introduction to Analytic Number Theory: Section 8.4: Pages 162-164: Multiplicative properties of the sums \( s_k(n) \) |
| 63 |
Fri, 18 Jun 2021 17:00 UTC |
40 mins |
14 |
Introduction to Analytic Number Theory: Section 8.5: Pages 165-166: Gauss sums associated with Dirichlet characters |
| 64 |
Mon, 21 Jun 2021 17:00 UTC |
40 mins |
12 |
Introduction to Analytic Number Theory: Sections 8.6-8.7: Pages 166-168: Dirichlet characters with nonvanishing Gauss sums, Induced moduli and primitive characters |
| 65 |
Tue, 22 Jun 2021 17:00 UTC |
40 mins |
11 |
Introduction to Analytic Number Theory: Section 8.8: Pages 168-170: Further properties of induced moduli |
| 66 |
Wed, 23 Jun 2021 17:00 UTC |
40 mins |
12 |
Introduction to Analytic Number Theory: Sections 8.9-8.10: Pages 171-173: The conductor of a character, Primitive characters and separable Gauss sums |
| 67 |
Thu, 24 Jun 2021 17:00 UTC |
40 mins |
11 |
Introduction to Analytic Number Theory: Sections 8.11-8.12: Pages 174-174: The donductor of a character, Primitive characters and separable Gauss sums |
| 68 |
Mon, 28 Jun 2021 17:00 UTC |
40 mins |
9 |
Introduction to Analytic Number Theory: Sections 9.1-9.2: Pages 178-180: Quadratic residues, Legendre's symbol and its properties |
| 69 |
Tue, 29 Jun 2021 17:00 UTC |
40 mins |
9 |
Introduction to Analytic Number Theory: Section 9.3: Pages 181-182: Evaluation of \( (-1 \mid p) \) and \( 2 \mid p \) |
| 70 |
Wed, 30 Jun 2021 17:00 UTC |
40 mins |
10 |
Introduction to Analytic Number Theory: Section 9.4: Pages 182-185: Gauss' lemma |
| 71 |
Thu, 01 Jul 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 9.5: Pages 185-187: The quadratic reciprocity law |
| 72 |
Fri, 02 Jul 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 9.7: Pages 187-190: The Jacobi symbol |
| 73 |
Tue, 06 Jul 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 9.8: Pages 190-192: Applications to Diophantine equations |
| 74 |
Wed, 07 Jul 2021 17:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Section 9.9: Pages 192-193: Gauss sums and the quadratic reciprocity law (Theorems 9.13-9.14) |
| 75 |
Thu, 08 Jul 2021 17:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Section 9.9: Pages 193-195: Gauss sums and the quadratic reciprocity law (Theorem 9.15) |
| 76 |
Fri, 09 Jul 2021 17:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Sections 9.10-9.11: Pages 195-201: The reciprocity law for quadratic Gauss sums, Another proof of the quadratic reciprocity law |
| 77 |
Tue, 13 Jul 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 10.1-10.3: Pages 204-206: The exponent of a number mod \( m, \) Primitive roots and reduced residue systems, The nonexistence of primitive roots mod \( 2^{\alpha} \) for \( \alpha \ge 3 \) |
| 78 |
Wed, 14 Jul 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 10.4-10.5: Pages 206-208: The existence of primitive roots mod \( p \) for odd primes \( p \) |
| 79 |
Thu, 15 Jul 2021 17:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Sections 10.6-10.7: Pages 208-210: The existence of primitive roots mod \( p^{\alpha}, \) The existence of primitive roots mod \( 2p^{\alpha} \) |
| 80 |
Fri, 16 Jul 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 10.8-10.9: Pages 211-212: The nonexistence of primitive roots in the remaining cases, The number of primitive roots mod \( m \) |
| 81 |
Tue, 20 Jul 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 10.10: Pages 213-217: The index calculus |
| 82 |
Wed, 21 Jul 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 10.11: Pages 218-219: Primitive roots and Dirichlet characters |
| 83 |
Thu, 22 Jul 2021 17:00 UTC |
40 mins |
6 |
Introduction to Analytic Number Theory: Section 10.12: Page 220: Real-valued Dirichlet characters mod \( p^{\alpha} \) |
| 84 |
Fri, 23 Jul 2021 17:00 UTC |
40 mins |
8 |
Introduction to Analytic Number Theory: Section 10.13: Pages 221-223: Primitive Dirichlet characters mod \( p^{\alpha} \) |
| 85 |
Tue, 27 Jul 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 11.1-11.2: Pages 224-225: The half-plane of absolute convergence of a Dirichlet series |
| 86 |
Wed, 28 Jul 2021 17:00 UTC |
40 mins |
6 |
Introduction to Analytic Number Theory: Sections 11.3-11.4: Pages 226-229: The function defined by a Dirichlet series, Multiplication of Dirichlet series |
| 87 |
Thu, 29 Jul 2021 17:00 UTC |
40 mins |
6 |
Introduction to Analytic Number Theory: Section 11.5: Pages 230-231: Euler products |
| 88 |
Fri, 30 Jul 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 11.5: Pages 231-232: Euler products (Examples) |
| 89 |
Tue, 03 Aug 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 11.6: Pages 232-234: The half-plane of convergence of a Dirichlet series |
| 90 |
Wed, 04 Aug 2021 17:00 UTC |
40 mins |
6 |
Introduction to Analytic Number Theory: Section 11.7: Pages 234-236: Analytic properties of Dirichlet series |
| 91 |
Thu, 05 Aug 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 11.8-11.9: Pages 236-239: Dirichlet series with nonnegative coefficients, Dirichlet series expressed as exponentials of Dirichlet series |
| 92 |
Fri, 06 Aug 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 11.8-11.10: Pages 240-241: Mean value formulas for Dirichlet series |
| 93 |
Tue, 10 Aug 2021 17:00 UTC |
40 mins |
6 |
Introduction to Analytic Number Theory: Section 11.11: Page 242: An integral formula for the coefficients of a Dirichlet series |
| 94 |
Wed, 11 Aug 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Section 11.12: Pages 243-245: An integral formula for the partial sums of a Dirichlet series (Lemma 4) |
| 95 |
Thu, 12 Aug 2021 17:00 UTC |
30 mins |
6 |
Introduction to Analytic Number Theory: Sections 11.12-12.1: Pages 245-250: An integral formula for the partial sums of a Dicihlet series (Theorem 11.18: Perron's formula), Hurwitz zeta function |
| 96 |
Fri, 13 Aug 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 12.2-12.3: Pages 250-252: Properties of the gamma function, Integral representation of the Hurwitz zeta function |
| 97 |
Tue, 17 Aug 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 12.4: Pages 253-254: A contour integral representation for the Hurwitz zeta function |
| 98 |
Wed, 18 Aug 2021 17:00 UTC |
40 mins |
6 |
Introduction to Analytic Number Theory: Sections 12.5-12.7: Pages 254-257: Analytic continuation of \( \zeta(s, a), \) \( \zeta(s), \) and \( L(s, \chi), \) Hurwitz's formula for \( \zeta(s, a) \) |
| 99 |
Thu, 19 Aug 2021 17:00 UTC |
35 mins |
6 |
Introduction to Analytic Number Theory: Sections 12.7: Pages 257-259: Hurwitz's formula |
| 100 |
Fri, 20 Aug 2021 17:00 UTC |
35 mins |
6 |
Introduction to Analytic Number Theory: Sections 12.8: Pages 259-260: The functional equation for the Riemann zeta function |
| 101 |
Tue, 24 Aug 2021 17:00 UTC |
40 mins |
6 |
Introduction to Analytic Number Theory: Sections 12.9-12.10: Pages 261-262: The functional equations for the Hurwitz zeta function and L-functions |
| 102 |
Wed, 25 Aug 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory: Sections 12.10-12.11: Pages 262-265: The functional equations for the L-functions, Evaluation of \( \zeta(-n, a) \) |
| 103 |
Thu, 26 Aug 2021 17:00 UTC |
40 mins |
6 |
Introduction to Analytic Number Theory: Section 12.12: Pages 265-266: Properties of Bernoulli numbers and Bernoulli polynomials |
| 104 |
Tue, 31 Aug 2021 17:00 UTC |
45 mins |
5 |
Introduction to Analytic Number Theory: Sections 12.12-12.13: Pages 267-268: Properties of Bernoulli numbers and Bernoulli polynomials, Formulas for \( L(0, \chi) \) |
| 105 |
Wed, 01 Sep 2021 17:00 UTC |
30 mins |
7 |
Introduction to Analytic Number Theory: Section 12.14: Pages 268-270: Approximation of \( \zeta(s, a) \) by finite sums |
| 106 |
Thu, 02 Sep 2021 17:00 UTC |
40 mins |
5 |
Introduction to Analytic Number Theory: Sections 12.15-12.16: Pages 270-273: Inequalities for \( \lvert \zeta(s, a) \rvert, \) \( \lvert \zeta(s) \rvert, \) and \( \lvert L(s, \chi) \rvert \) |
| 107 |
Fri, 03 Sep 2021 17:00 UTC |
40 mins |
5 |
Introduction to Analytic Number Theory: Sections 13.1-13.2: Pages 278-281: The plan of the proof, Lemmas |
| 108 |
Tue, 07 Sep 2021 17:00 UTC |
40 mins |
6 |
Introduction to Analytic Number Theory: Sections 13.2-13.3: Pages 281-284: Lemmas, A contour integral representation for \( \psi_1(x)/x^2 \) |
| 109 |
Wed, 08 Sep 2021 17:00 UTC |
40 mins |
5 |
Introduction to Analytic Number Theory: Sections 13.4-13.5: Pages 284-287: Upper bounds for \( \zeta(s) \) and \( \zeta'(s) \) near the line \( \sigma = 1, \) The nonvanishing of \( \zeta(s) \) on the line \( \sigma = 1 \) |
| 110 |
Thu, 09 Sep 2021 17:00 UTC |
40 mins |
4 |
Introduction to Analytic Number Theory: Sections 13.6-13.7: Pages 287-291: Inequalities for \( 1/\zeta(s) \) and \( \zeta'(s)/\zeta(s), \) Completion of the proof of the prime number theorem |
| 111 |
Tue, 14 Sep 2021 17:00 UTC |
40 mins |
5 |
Introduction to Analytic Number Theory: Sections 13.8-13.9: Pages 291-293: Zero-free regions for \( \zeta(s), \) The Riemann Hypothesis |
| 112 |
Wed, 15 Sep 2021 17:00 UTC |
40 mins |
5 |
Introduction to Analytic Number Theory: Section 13.10: Pages 294-296: Applications to the divisor function |
| 113 |
Thu, 16 Sep 2021 17:00 UTC |
40 mins |
4 |
Introduction to Analytic Number Theory: Section 13.11: Pages 297-299: Application to Euler's totient |
| 114 |
Fri, 17 Sep 2021 17:00 UTC |
40 mins |
4 |
Introduction to Analytic Number Theory: Sections 13.12-14.2: Pages 299-307: Extension of Pólya's inequality for character sums, Geometric representation of partitions |
| 115 |
Tue, 21 Sep 2021 17:00 UTC |
30 mins |
4 |
Introduction to Analytic Number Theory: Section 14.3: Pages 308-310: Generating functions for partitions |
| 116 |
Wed, 22 Sep 2021 17:00 UTC |
35 mins |
4 |
Introduction to Analytic Number Theory: Section 14.4: Pages 311-313: Euler's pentagonal-number theorem |
| 117 |
Tue, 28 Sep 2021 17:00 UTC |
45 mins |
8 |
Introduction to Analytic Number Theory: Sections 14.5-14.7: Pages 313-318: Combinatorial proof of Euler's pentagonal-number theorem, Euler's recursion formula for \( p(n), \) An upper bound for \( p(n) \) |
| 118 |
Wed, 29 Sep 2021 17:00 UTC |
45 mins |
6 |
Introduction to Analytic Number Theory: Section 14.8: Pages 318-320: Jacobi's triple product identity |
| 119 |
Thu, 30 Sep 2021 17:00 UTC |
40 mins |
5 |
Introduction to Analytic Number Theory: Sections 14.9-14.10: Pages 321-322: Consequences of Jacobi's identity, Logarithmic differentiation of generation functions |
| 120 |
Fri, 01 Oct 2021 17:00 UTC |
35 mins |
7 |
Introduction to Analytic Number Theory: Sections 14.10-14.11: Pages 323-324: Recursion formula for \( p_{A,f}(n), \) The partition identities of Ramanujan |