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Università degli Studi di Parma Università degli Studi di Parma
Second cycle degree course in
Mathematics
Università degli Studi di Parma
Department of Mathematical, Physical and Computer Sciences

NUMBER THEORY
cod. 1001172

Academic year 2022/23
1° year of course - First semester
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
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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

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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

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2030 agenda goals for sustainable development

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