Learning objectives
An overview of the most important problems of the <br />
discipline
Prerequisites
# <br />
Functions of one variable A and B, Topology and complex variable
Course unit content
<br />1. Distribution of prime numbers: Chebyshev’s theorems, Mertens formulae, Selberg’s formulae. <br />
2. Basic arithmetic functions, multiplicative functions and completely multiplicative functions, Dirichlet product and hyperbola method. <br />
3. Sieve methods: mention of Brun’s combinatorial sieve and its applications. <br />
4. The large sieve and a few applications. <br />
5. Riemann zeta function and its properties, mention of the analytical demonstration of the Prime Number Theorem. <br />
6. Mention of the Goldbach problem and the circle method.
Bibliography
1. T. M. APOSTOL, Introduction to Analytic Number Theory,Springer, Berlino, 1975. <br />
2. K. CHANDRASEKHARAN, Introduction to Analytic Number Theory,Springer, Berlino, 1968. <br />
3. H. DAVENPORT, Multiplicative Number Theory, terza edizione,Springer, Berlino, 2001. <br />
4. G. H. HARDY & E. M. WRIGHT,An Introduction to the Theory of Numbers, fifth edition, Oxford Science Publications, Oxford, 1979. <br />
5. L. K. HUA, Introduction to Number Theory, Springer, Berlino, 1982. <br />
6. E. LANDAU, Elementary Number Theory, Chelsea, New York, 1960.