M8195 Number theory seminar

Faculty of Science
Autumn 2025
Extent and Intensity
0/2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: z (credit).
In-person direct teaching
Teacher(s)
Mgr. Pavel Francírek, Ph.D. (lecturer)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 14:00–15:50 M6,01011
Prerequisites
The knowledge of algebra and rudiments of Galois theory in the range of M3150 Algebra II are necessary. Understanding the basics of algebraic number theory would be useful (for example in the range of the two previous semesters of this seminar).
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Abstract
In this semester we will build on the knowledge gained in previous semesters. Our main goal will be the study of p-adic L-functions.
Learning outcomes
At the end of this course, students should be able to:
define basic notions of the studied theory;
explain learned theoretical results;
apply learned methods to concrete exercises.
Key topics
  • Dirichlet L-functions (complex variable);
  • construction of p-adic L-functions by the Kubota-Leopoldt method using Bernoulli numbers;
  • Iwasawa's construction of p-adic L-functions.
Study resources and literature
  • WASHINGTON, Lawrence C. Introduction to cyclotomic fields. 2nd ed. New York: Springer, 1997, xiv, 487. ISBN 0387947620. info
  • ROSEN, Michael I. A classical introduction to modern number theory. Edited by Kenneth F. Ireland. 2nd ed. New York: Springer, 1990, xiv, 389. ISBN 354097329X. info
Bookmarks
https://is.muni.cz/ln/tag/PříF:M8195!
Approaches, practices, and methods used in teaching
In this semester, we will meet in person. Home preparation will play an important role.
Method of verifying learning outcomes and course completion requirements
Credit will be given in case of active work in seminars - the study of the mentioned book during the term, regular solving of homework.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught each semester.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2010 - only for the accreditation, Spring 2005, Autumn 2005, Spring 2006, Autumn 2006, Spring 2007, Autumn 2007, Spring 2008, Autumn 2008, Spring 2009, Autumn 2009, Spring 2010, Autumn 2010, Spring 2011, Autumn 2011, Spring 2012, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Spring 2013, Autumn 2013, Spring 2014, Autumn 2014, Spring 2015, Autumn 2015, Spring 2016, Autumn 2016, Spring 2017, autumn 2017, spring 2018, Autumn 2018, Spring 2019, Autumn 2019, Spring 2020, Autumn 2020, Spring 2021, autumn 2021, Spring 2022, Autumn 2022, Spring 2023, Autumn 2023, Spring 2024, Autumn 2024, Spring 2025, Spring 2026.
  • Enrolment Statistics (Autumn 2025, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2025/M8195