| # |
Date |
Duration |
Participants |
Topic |
| 1 |
Fri, 05 Mar 2021 15:30 UTC |
40 mins |
4 |
Introduction to Analytic Number Theory (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): Sections 1.2; Page 14; Divisibility (Recap) |
| 4 |
Mon, 08 Mar 2021 18:00 UTC |
40 mins |
6 |
Introduction to Analytic Number Theory (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): Section 2.14; Pages 39-40; Generalized convolutions |
| 17 |
Wed, 24 Mar 2021 18:00 UTC |
30 mins |
11 |
Introduction to Analytic Number Theory (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): Section 5.3; Pages 110-113; Linear congruences |
| 42 |
Tue, 11 May 2021 18:00 UTC |
40 mins |
10 |
Introduction to Analytic Number Theory (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): Section 6.8; Pages 137-140; Dirichlet characters |
| 54 |
Tue, 01 Jun 2021 18:00 UTC |
40 mins |
9 |
Introduction to Analytic Number Theory (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): Section 9.4; Pages 182-185; Gauss' lemma |
| 71 |
Thu, 01 Jul 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): Section 11.5; Pages 230-231; Euler products |
| 88 |
Fri, 30 Jul 2021 17:00 UTC |
40 mins |
7 |
Introduction to Analytic Number Theory (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): 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 (Apostol, 1976): Sections 14.9-14.10; Pages 321-322; Consequences of Jacobi's identity, Logarithmic differentiation of generationf functions |
| 120 |
Fri, 01 Oct 2021 17:00 UTC |
35 mins |
7 |
Introduction to Analytic Number Theory (Apostol, 1976): Sections 14.10-14.11; Pages 323-324; Recursion formula for \( p_{A,f}(n) \), The partition identities of Ramanujan |