- Docente: Marilena Barnabei
- Credits: 6
- SSD: MAT/02
- Language: Italian
- Moduli: Marilena Barnabei (Modulo 1) Marta Morigi (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
Course contents
Integer partitions. Ferrers diagrams. Euler Theorem about the generating function of the sequence p(n)= number of partitions of n. Gaussian binomial coefficients. Pentagonal numbers and Euler formula. Residues mod n. Euler and Moebius functions and their properties. Modular equations. Quadratic residues and Legendre symbol. Factorization methods. Primality tests. Pythagorean triples. Arithmetic functions. Dirichlet product. Multiplicative and completely multiplicative functions. Cyclotomic polynomial. Distribution function of an arithmetic function. First properties of algebraic integers.
Readings/Bibliography
Tom M. Apostol: Introduction to Analytic Number Theory - Springer, 2010
Marilena Barnabei - Flavio Bonetti: Elementi di aritmetica modulare - Esculapio, Bologna, 2014
Teaching methods
Teaching at the blackboard.
Office hours
See the website of Marilena Barnabei
See the website of Marta Morigi
SDGs
This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.