AIS - Analytic Methods in Algebraic Number Theory

Speakers and Syllabus


Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

Dr. Ekata Saha,
IIT Delhi, New Delhi

3

Prerequisites from algebraic number theory: Integral basis, Dirichlet unit theorem, class group and class number, discriminant, different

Dr. Sneha Chaubey,
IIIT Delhi, New Delhi

3

Prerequisites from analytic number theory: Riemann zeta function, Dirichlet L-functions, Euler product, functional equations, zero-free regions

Dr. Biswajyoti Saha,
IIT Delhi, New Delhi

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,
IMSc, Chennai

4

Theory of Dedekind zeta function: Dedekind zeta function, functional equation, analytic class number formula, asymptotic distribution of ideals

Prof. M. Ram Murty,
Queen’s University, Canada

4

TheoryofArtinL-series:ArtinL-series,Artin’sconjecture,Aramata- Brauer theorem, Artin symbol, Artin conductor, meromorphiccontinuation

Prof. Purusottam Rath,
CMI, Chennai

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,
University of Toronto, Canada

4

Effective Brauer-Siegel theorem: Explicit formulas, instances of effective Brauer-Siegel theorem andapplications

 

References:

  1. Serge Lang, Algebraic Number Theory, Springer New York,NY.

  2. Jean-Pierre Serre, Linear Representations of Finite Groups, Springer New York,NY.

  3. Harold Davenport, Multiplicative Number Theory, Springer New York,NY.

  4. Lawrence C. Washington, Introduction to Cyclotomic Fields, Springer New York,NY.

  5. Jürgen Neukirch, Algebraic Number Theory, Springer Berlin,Heidelberg.

  6. Harold Stark, Some effective cases of the Brauer-Siegel Theorem. Invent Math 23,135-152.

  7. 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
to
11.25)

Lecture 2

(11.30–1.00)

Lunch (1.05
to
2.25)

Tutorial (2.30–3.30)

Tea
(3.35
to
3.55)

Tutorial (4.00-5.00)

Snacks (5.05
to
5.30)

 

 

(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

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