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:

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 (with names of speakers and course associates/tutors):

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Full forms for the abbreviations of speakers and tutors:

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