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Centre International de Mathématiques Pures et Appliquées (CIMPA)

An L-function is a function defined additively by a Dirichlet series with a multiplicative Euler product. The initial work of Dirichlet was generalized to number fields by Hecke and given an adelic interpretation by Tate which paved the way to move from GL(1) to higher degree L functions associated to automorphic forms of GL(n) for a general n . Automorphic L functions are essentially analytic objects and allow translations between arithmetic and analysis. We recall the legendary correspondence in the case of the Riemann-ζ function, the prototype of higher L -functions both analytic and arithmetic-algebraic, between an arithmetic statement on the distribution of primes and an analytic one on the distribution of its zeros. Now there are many more parameters to explore. For example, bounding twisted automorphic forms in terms of conductors help obtain the asymptotics of representations of totally positive integers by ternary quadratic forms. The aim of this school is to prepare the participants to appreciate the contemporary theory of automorphic representations, their L -functions and their surprising links with diverse fields like Fourier analysis, algebraic geometry and theoretical physics.

The conference aims at bringing the eminent Number Theorists worldwide in the domain of Algebraic Number Theory and young scholars from the country on a common platform to project their work, and foster collaborations to further the development of Mathematical Research.

The areas of particular interest include: Ideal class groups of number fields (algebraic, analytic and computational aspects), Relative class numbers of number fields, Annihilators of class groups, Class field theory, Picard groups, Selmer groups, Diophantine equations, Elliptic curves, Iwasawa Theory, Modular forms and related topics.

Number Theory, Arithmetic,    Group Theory