Topics in the theory of numbers (graduate-level course)
IME, USP, Our first class: Tuesday, September 1, 2020, 14:00-16:00
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This is a graduate-level course which consists of an introduction to the analytic theory of numbers.
Some of the main topics we will cover include:
Advanced Linear Algebra
Dirichlet L-functions
Eementary Fourier analysis on the d-dimensional cube [0, 1]^d
The Riemann zeta function and its functional equation
Dirichlet's theorem concerning primes in arithmetic progressions
Group characters for finite abelian groups
Theta functions, and applications.
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GRADING: Homework = 100%
REFERENCES:
1. Tom Apostol, Introduction to analytic Number Theory, Springer UTM series, 1998.
2. Tom Apostol, Modular functions and Dirichlet series in Number Theory, Springer GTM series, 2'nd edition, 2012.
3. Matthias Beck and Sinai Robins, Computing the continuous discretely: integer point enumeration in polytopes,
2'nd edition, 2015.
4. Edmund Hlawka, Johannes Schoissengeier, Rudolf Taschner, Geometric and analytic number theory, 2012.
5. Ram Murty, Problems in analytic number theory, Springer GTM series, 2007.
- Docente: Sinai Robins