Mathematics | University of Parma

Professor: - Alessandro ZACCAGNINI
Academic discipline: Analisi matematica (MAT/05)
Field: Attività formative affini o integrative
Type of training activity: Related/supplementary

48 hours
of face-to-face activities

6 credits

hub:

course unit
in - - -

lectures timetable unavailable

exam calls

Learning objectives

Basic knowledge of Analytic Number Theory

Prerequisites

Basic calculus, basic complex analysis

Course unit content

Distribution of prime numbers: Chebyshev's theorems, Mertens's formulas, Selberg's formulas.
Elementary arithmetical functions: Multiplicative and totally multiplicative functions, Dirichlet product and the hyperbola method.
Sieve Methods: Sketch of Brun's combinatorial sieve and some applications.
The large sieve and its applications.
The Riemann zeta function and some properties, sketch of the analytic proof of the Prime Number Theorem.
Goldbach's problem: additive problems and the circle method.

Full programme

- - -

Bibliography

T. M. APOSTOL, Introduction to Analytic Number Theory, Springer, Berlino, 1975.
K. CHANDRASEKHARAN, Introduction to Analytic Number Theory, Springer, Berlino, 1968.
H. DAVENPORT, Multiplicative Number Theory, terza edizione, Springer, Berlino, 2001.
H. M. EDWARDS, Riemann's Zeta Function, Academic Press, 1974. Ristampa Dover, 2001.
G. H. HARDY & E. M. WRIGHT, An Introduction to the Theory of Numbers, quinta edizione, Oxford Science Publications, Oxford, 1979.
L. K. HUA, Introduction to Number Theory, Springer, Berlino, 1982.
E. LANDAU, Elementary Number Theory, Chelsea, New York, 1960.
H. L. MONTGOMERY & R. C. VAUGHAN, Multiplicative Number Theory. I. Classical Theory, Cambridge University Press, Cambridge, 2006.

Teaching methods

Classical lecture

Assessment methods and criteria

A lecture on a topic chosen by the student

Other information