2019 Advanced courses in Algebra D

Font size  SML

Register update notification mail Add to favorite lecture list
Academic unit or major
Mathematics
Instructor(s)
Suzuki Masatoshi 
Course component(s)
Lecture
Day/Period(Room No.)
Thr5-6(H137)  
Group
-
Course number
ZUA.A334
Credits
1
Academic year
2019
Offered quarter
4Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

This course follows Advanced topics in Algebra C.

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. Based on Advanced topics in Algebra C, we study more general L-functions defined axiomatically.

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

Axiomatic definition of L-functions, analytic properties of L-functions, Selberg trace formula, Weil's 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 Axiomatic definition of L-functions Details will be provided during each class session
Class 2 Analytic properties of L-functions Details will be provided during each class session
Class 3 Generalized Riemann hypothesis and other conjecturtes Details will be provided during each class session
Class 4 Selberg trace formula Details will be provided during each class session
Class 5 Selberg zeta functions Details will be provided during each class session
Class 6 Weil's explicit formula Details will be provided during each class session
Class 7 Spectral interpretation of zeros I Details will be provided during each class session
Class 8 Spectral interpretation of zeros II Details will be provided during each class session

Textbook(s)

None required

Reference books, course materials, etc.

H. Iwaniec and E. Kowalski, Analytic number theory, Colloquium Publications, 53, AMS
H. Iwaniec and P. Sarnak, Perspectives on the analytic theory of L-functions, Geom. Funct. Anal. 2000, 705-741

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.A333 : Advanced courses in Algebra C

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

Basic undergraduate algebra and complex analysis

Other

None in particular.

Page Top