Details of MA5219 (Spring 2025)
| Level: 5 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA5219 | Analytic Number Theory | Soumya Bhattacharya |
| Syllabus |
|---|
| Divergence of the sum of the reciprocals of the primes, Chebyshevs estimates for the prime counting function, Bertrands postulate.
Dirichlet convolution, Moebius inversion formula, the ring of arithmetic functions, Dirichlets hyperbola method, analytic properties of Dirichlet series, Mertens three estimates, properties of the Riemann Zeta function, Dirichlets theorem on primes in arithmetic progression, the Prime Number Theorem. Elements of Sieve Theory, the sieve of Eratostenes, the Brun sieve, convergence of the sum of the reciprocals of the twin primes. Modular groups, classical modular functions and modular forms, the fundamental domain of the full modular group, the valence formula, the dimension of the space of modular forms, cusp forms, Hecke operators. |
| Prerequisite |
|---|
| Prerequisites:
1. Algebra III (MA4101) 2. Representation Theory of Finite Groups (MA4204) 3. Topics in Complex Analysis (MA5106) |
| References |
|---|
| Textbooks:
1. Luca F., De Koninck J-M., Analytic Number Theory 2. Iwaniec H., Kowalski E., Analytic Number Theory 3. Bruinier J-H., van der Geer G., Harder G., Zagier D., The 1-2-3 of Modular Forms References: 1. Davenport H., Multiplicative Number Theory 2. Serre J-P., A Course in Arithmetic 3. Ireland K., Rosen M., A Classical Introduction to Modern Number Theory 4. Tenenbaum G., Introduction to Analytic and Probabilistic Number Theory 5. Koukoulopoulos D., The Distribution of Prime Numbers 6. Friedlander J., Iwaniec H., Opera de Cribro 7. Apostol T., Introduction to Analytic Number Theory |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Not Allowed |
| 3 | IP | 6 | Not Allowed |
| 4 | MP | 2 | Not Allowed |
| 5 | MP | 4 | Elective |
| 6 | MR | 2 | Not Allowed |
| 7 | MR | 4 | Not Allowed |
| 8 | MS | 10 | Elective |
| 9 | MS | 4 | Not Allowed |
| 10 | MS | 6 | Not Allowed |
| 11 | MS | 8 | Not Allowed |
| 12 | RS | 1 | Elective |
| 13 | RS | 2 | Elective |