(in Polish) Analytic Number Theory 1000-1M26ANT
Full description:
1. Elementary methods (Euler, product, Abel partial summation)
2. Prime number theorem (PNT)
3. Euler gamma function
4. Riemann zeta function, Riemann functional equation
5. Hadamard factorization
6. Quantitative PNT, Riemann hypothesis (RH), equivalence of RH with distribution of primes (von Koch's theorem)
7. Primes in arithmetic progressions, Dirichlet characters, Dirichlet's theorem
8. PNT for arithmetic progressions
9. Functional equation for L(s,x), primitive characters
10. Quantitative PNT for arithmetic progressions
11. Zero-free region for L(s,x), exceptional zeros
12. Siegel and Siegel-Walfisz theorems
13. Lindelöf hypothesis
Type of course
Requirements
Assessment criteria
Assessment methods and assessment criteria:
An oral exam. The final grade will be heavily influenced by the student's active participation in exercise classes.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes: