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Number Theory
Last Updated: 2026-02-05 15:23:57
Abstract
Generating series;Partition counting (Hardy-Ramanujan asymptotics, Jacobi Triple Product, Euler Pentagonal Number Theorem, Ramanujan congruences, Rogers-Ramanujan identities);Transcendence theory (general principles, Liouville, Hermite, Lindaman, Roth and Gelfond-Schneider theorems, transcendence of e and pi);Waring's probem;Dirichlet's theorem on primes in arithmetic progression
Objective
Generating series; Partition counting (Hardy-Ramanujan asymptotics, Jacobi Triple Product, Euler Pentagonal Number Theorem, Ramanujan congruences, Rogers-Ramanujan identities); Transcendence theory (general principles, Liouville, Hermite, Lindaman, Roth and Gelfond-Schneider theorems, transcendence of e and pi); Waring's probem; Dirichlet's theorem on primes in arithmetic progression
Resources
Literature
Many sources, but in particular: - Donald J. Newmand: Analytic Number Theory (generating series, asymptotics of partitions, Waring's problem) - Burger + Tubbs: Making Transcendence Transparent (transcendence) - Everest + Ward: An introduction to Number Theory (Dirichlet's theorem on primes in arithmetic progressions)
General Information
- Language
- English
- Levels
- BSC , MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Number Theory |
|
2 h weekly |