Fall Quarter 2019
Hecke L-functions and their critical values
Meeting Time: Mondays, Wednesdays and Fridays 2:00pm to
2:50pm in MS 7608.
Office hours: After class meetings, from 3 PM (MW) until 3:50 PM
in my office: MS6308.
Lecture Starts on Monday September 30th at 2 PM in MS 7608
Texts: Lecture notes will be posted:
Grading will be based on student presentation at the end of courses on topics close to the course material.
No final exam is planned.
[Note No.0] (posted, a pdf file),
[Note No.1] (posted, a pdf file),
[Note No.2] (posted, a pdf file),
[Note No.3] (posted, a pdf file),
[Note No.4] (posted, a pdf file),
[Note No.5] (posted, a pdf file, last lecture notes).
we suggest[LFE] H. Hida, "Elementary Theory of L-functions
and Eisenstein Series",
LMSST 26, Cambridge University Press, 1993,
[EDM] G. Shimura, "Elementary Dirichlet series and Modular forms", Springer Monographs in Mathematics, Springer 2007.
Topics: In this course, assuming basic knowledge
of complex analysis,
we describe the proof of Euler/Hurwitz/Shintani of rationality of Hecke L-values at non-positive integers.
We hope to cover the following four topics:
Analytic continuation/functional equation of Dirichlet L functions,
Analytic continuation/functional equation of Hecke L functions over totally real field (and possibly over general number fields),
Rationality and integrality of L-values,
If time allows, construction of Kubota-Leopoldt and Deligne-Ribet p-adic L functions.
Good understanding of complex analysis (for Riemann surfaces) and
basics of algebraic number theory (e.g. Dirichlet's unit theorem).