CODE 84023 ACADEMIC YEAR 2022/2023 CREDITS 6 cfu anno 3 MATEMATICA 8760 (L-35) - GENOVA 6 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 2 MATEMATICA 9011 (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 SANDRO BETTIN Ricevimento: By appointment Exam Board SANDRO BETTIN (President) MARC ALEXANDRE MUNSCH ALBERTO PERELLI (President Substitute) LESSONS Class schedule L'orario di tutti gli insegnamenti è consultabile all'indirizzo EasyAcademy. EXAMS EXAM DESCRIPTION Written and oral exam ASSESSMENT METHODS Written exam and oral exam on parts of the program Exam schedule Data Ora Luogo Degree type Note 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