28442 - Number Theory 1

Course Unit Page

Academic Year 2018/2019

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. Prime number theorem (without proof). Riemann Zeta function and its elementary properties.

 

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


Assessment methods


Office hours

See the website of Marilena Barnabei