2019 Advanced courses in Algebra C

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Academic unit or major
Mathematics
Instructor(s)
Suzuki Masatoshi 
Course component(s)
Lecture
Day/Period(Room No.)
Thr5-6(H137)  
Group
-
Course number
ZUA.A333
Credits
1
Academic year
2019
Offered quarter
3Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

This course is an introduction to analytic number theory. Particularly, we will study modern tools and concepts in the theory of zeta- and L-functions. This course is followed by Advanced topics in Algebra D.

Zeta- and L-functions appear in many areas of number theory, and are studied very actively. This course hopes to provide solid background for students intending to learn advanced topics on zeta- and L-functions. We begin with the classical Riemann zeta function.

Student learning outcomes

Students are expected to:
-- understand fundamental notions and methods of analytic number theory
-- be familiar with modern tools and concepts in the theory of zeta- and L-functions.

Keywords

Riemann zeta function, functional equation, Prime Number Theorem, zero-free region, explicit formula

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
- - - -

Class flow

This is a standard lecture course. There will be some assignments.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Riemann zeta function Details will be provided during each class session
Class 2 Analytic continuation and functional equation Details will be provided during each class session
Class 3 Special values Details will be provided during each class session
Class 4 Partial summation formula Details will be provided during each class session
Class 5 Prime Number Theorem Details will be provided during each class session
Class 6 Zero-free region Details will be provided during each class session
Class 7 Proof of the Prime Number Theorem Details will be provided during each class session
Class 8 Explicit formula Details will be provided during each class session

Textbook(s)

None required

Reference books, course materials, etc.

H. Davenport, Multiplicative Number Theory, GTM 74 (3rd revised ed.), New York: Springer-Verlag
H. L. Montgomery and R. C. Vaughan, Multiplicative Number Theory I : Classical Theory, CSAM 97. Cambridge University Press

Assessment criteria and methods

Course scores are evaluated by homework assignments (100%). Details will be announced during the course.

Related courses

  • MTH.A407 : Advanced topics in Algebra C1
  • MTH.A408 : Advanced topics in Algebra D1
  • ZUA.A334 : Advanced courses in Algebra D

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Basic undergraduate algebra and complex analysis

Other

None in particular.

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