AIS - Analytic Methods in Algebraic Number Theory
Speakers and Syllabus
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
Dr. Ekata Saha, |
3 |
Prerequisites from algebraic number theory: Integral basis, Dirichlet unit theorem, class group and class number, discriminant, different |
Dr. Sneha Chaubey, |
3 |
Prerequisites from analytic number theory: Riemann zeta function, Dirichlet L-functions, Euler product, functional equations, zero-free regions |
Dr. Biswajyoti Saha, |
2 |
Prerequisites from representation theory of groups: Character of a representation, regular representation, Frobenius reciprocity, Artin’s theorem, p-elementary subgroups, Brauer’s theorem. |
Prof. Sanoli Gun, |
4 |
Theory of Dedekind zeta function: Dedekind zeta function, functional equation, analytic class number formula, asymptotic distribution of ideals |
Prof. M. Ram Murty, |
4 |
TheoryofArtinL-series:ArtinL-series,Artin’sconjecture,Aramata- Brauer theorem, Artin symbol, Artin conductor, meromorphiccontinuation |
Prof. Purusottam Rath, |
4 |
Siegel’s theorem and Brauer’s extension: Siegel’s theorem, ineffectivity in Siegel’s theorem, Brauer’s extension of Siegel’s theorem |
Prof. V. Kumar Murty, |
4 |
Effective Brauer-Siegel theorem: Explicit formulas, instances of effective Brauer-Siegel theorem andapplications |
References:
-
Serge Lang, Algebraic Number Theory, Springer New York,NY.
-
Jean-Pierre Serre, Linear Representations of Finite Groups, Springer New York,NY.
-
Harold Davenport, Multiplicative Number Theory, Springer New York,NY.
-
Lawrence C. Washington, Introduction to Cyclotomic Fields, Springer New York,NY.
-
Jürgen Neukirch, Algebraic Number Theory, Springer Berlin,Heidelberg.
-
Harold Stark, Some effective cases of the Brauer-Siegel Theorem. Invent Math 23,135-152.
-
V. Kumar Murty, Class numbers of CM-fields with solvable normal closure, Compositio Math. 127,273-287.
Time Table
Time-Table (with names of speakers and course associates/tutors):
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.05 |
Lecture 2 (11.30–1.00) |
Lunch (1.05 |
Tutorial (2.30–3.30) |
Tea |
Tutorial (4.00-5.00) |
Snacks (5.05 |
|
|
(name of the speaker) |
|
(name of the speaker) |
|
(name of the speaker + tutors) |
|
(name of the speaker + tutors) |
|
Mon |
4/12/23 |
ES |
|
SC |
|
SC, BM, PSM |
|
ES, AG, DK |
|
Tues |
5/12/23 |
ES |
|
SC |
|
SC, BM, PSM |
|
ES, AG, DK |
|
Wed |
6/12/23 |
ES |
|
SC |
|
SC, BM, PSM |
|
ES, AG, DK |
|
Thu |
7/12/23 |
BS |
|
SG |
|
BS, AG, BM |
|
SG, DK, DS |
|
Fri |
8/12/23 |
BS |
|
SG |
|
BS, AG, BM |
|
SG, DK, DS |
|
Sat |
9/12/23 |
RM |
|
PR |
|
RM, RL, SH |
|
PR, P, PSM |
|
SUNDAY: OFF |
|||||||||
Mon |
11/12/23 |
RM |
|
SG |
|
RM, RL, SH |
|
SG, DK, DS |
|
Tues |
12/12/23 |
PR |
|
SG |
|
PR, P, PSM |
|
SG, DK, DS |
|
Wed |
13/12/23 |
PR |
|
KM |
|
PR, P, SH |
|
KM, BS, RL |
|
Thu |
14/12/23 |
RM |
|
KM |
|
RM, DS, SH |
|
KM, BS, RL |
|
Fri |
15/12/23 |
RM |
|
KM |
|
RM, DS, SH |
|
KM, BS, RL |
|
Sat |
16/12/23 |
PR |
|
KM |
|
PR, P, SH |
|
KM, BS, RL |
|
Tutorial Assistants:
S. No. |
Name |
Affiliation |
1 |
Akanksha Gupta |
IIT Delhi, New Delhi |
2 |
Bikram Misra |
IIT Delhi, New Delhi |
3 |
Divyanshu Kala |
IIT Delhi, New Delhi |
4 |
Dhananjaya Sahu |
IMSc, Chennai |
5 |
Pawan Singh Mehta |
IIT Delhi, New Delhi |
6 |
Preeti |
CMI, Chennai |
7 |
Rashi Lunia |
IMSc, Chennai |
8 |
Suhita Hazra |
CMI, Chennai |
Full forms for the abbreviations of speakers and tutors:
-
BS:
Biswajyoti Saha
AG:
Akanksha Gupta
ES:
Ekata Saha
BM:
Bikram Misra
KM:
V. Kumar Murty
DK:
Divyanshu Kala
PR:
Purusottam Rath
DS:
Dhananjaya Sahu
RM:
M. Ram Murty
PSM:
Pawan Singh Mehta
SC:
Sneha Chaubey
P:
Preeti
SG:
Sanoli Gun
RL:
Rashi Lunia
SH:
Suhita Hazra