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ANALITYC NUMBER THEORY

CODE 84023
ACADEMIC YEAR 2022/2023
CREDITS
  • 6 cfu during the 3nd year of 8760 MATEMATICA (L-35) - GENOVA
  • 6 cfu during the 1st year of 9011 MATEMATICA(LM-40) - GENOVA
  • 6 cfu during the 2nd year of 9011 MATEMATICA(LM-40) - GENOVA
  • SCIENTIFIC DISCIPLINARY SECTOR MAT/05
    TEACHING LOCATION
  • GENOVA
  • SEMESTER 1° Semester
    TEACHING MATERIALS AULAWEB

    OVERVIEW

    The course will give an introduction to analytic number theroy.

    The lecture will be in Italian unless requested otherwise by the students.

     

    AIMS AND CONTENT

    LEARNING OUTCOMES

    The aim of the course is to introduce basic elementary and analytical concepts, and the relative techniques, for the study of arithmetic problems, in particular concerning prime numbers. The course provides analytical prerequisites necessary to address more advanced issues in Number Theory, Arithmetic Geometry and related topics.

    PREREQUISITES

    It is useful to have some basic knowledge of complex analysis.

    TEACHING METHODS

    Traditional

    SYLLABUS/CONTENT

    Arithmetical functions: arithmetical and algebraic aspects, asymptotic behavior. Elementary methods for the distribution of primes: Euler, Legendre and Chebyshev. Elements of cryptography. Complements of Analysis: Dirichlet series, Mellin transform and Poisson formula. Riemann zeta function: general properties and distribution of zeros. Prime Number Theorem: explicit formulae and PNT with remainder. Dirichlet L-functions: Dirichlet characters, general properties of L-functions and distribution of zeros. Dirichlet's theorem.

     

    RECOMMENDED READING/BIBLIOGRAPHY

    Course notes.

    A.E.Ingham - The Distribution of Prime Numbers - Cambridege U.P. 1964.

    H.Davenport - Multiplicative Number Theory - Springer 1980.

    G.Tenenbaum, M.Mendes-France - The Prime Numbers and Their Distribution - AMS 2000.

    G.Tenenbaum - Introduction to Analytic and Probabilistic Number Theory - Cambridge U.P., 1995

     

    TEACHERS AND EXAM BOARD

    Exam Board

    SANDRO BETTIN (President)

    MARC ALEXANDRE MUNSCH

    ALBERTO PERELLI (President Substitute)

    LESSONS

    Class schedule

    All class schedules are posted on the EasyAcademy portal.

    EXAMS

    EXAM DESCRIPTION

    Written and oral exam

     

    ASSESSMENT METHODS

    Written exam and oral exam on parts of the program

     

    Exam schedule

    Date Time Location Type Notes
    10/01/2023 09:30 GENOVA Scritto
    12/01/2023 14:30 GENOVA Orale
    31/01/2023 09:30 GENOVA Scritto
    02/02/2023 14:30 GENOVA Orale
    08/06/2023 09:30 GENOVA Scritto
    08/06/2023 14:30 GENOVA Orale
    06/07/2023 09:30 GENOVA Scritto
    06/07/2023 14:30 GENOVA Orale
    14/09/2023 09:30 GENOVA Scritto
    14/09/2023 14:30 GENOVA Orale