Limit Conjectures in Number Theory, Lehmer's Conjecture, Conjecture of Schinzel-Zassenhaus, dynamical zeta function of the beta-shift - Archive ouverte HAL Accéder directement au contenu
Vidéo Année : 2018

Limit Conjectures in Number Theory, Lehmer's Conjecture, Conjecture of Schinzel-Zassenhaus, dynamical zeta function of the beta-shift

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Résumé

This Summer School on the Theory of Motives and the Theory of Numbers, at the crossroad of several L functions, zeta functions, polyzeta functions and dynamical zeta functions will be held on the scientific campus of Le-Bourget-du-Lac, close to the Department of Mathematics (LAMA) of the University Savoie Mont Blanc, from June 18th till June 29th 2018. It is one of the thematic Schools of the CNRS whose main objective is to gather young researchers working in these domains, whose details can be found in the mini-courses. The topics of the mini-courses are closely related but often progress in parallel. The idea of this Summer School is to make them live in a transversal way. Several domains are concerned : in Geometry, singularity theory, model theory, o-minimality, motive theory, Igusa zeta functions, in Number Theory. p-adic and complex L functions on classical groups, Dirichlet series and zeta functions of one and several variables, in Dynamics of algebraic numbers, on Perron numbers, dynamical zeta functions of the beta-shift. The questions of rationality, of zeroes, of poles, of natural boundary, are often common to zeta, polyzeta, L functions.

Dates et versions

hal-03146682 , version 1 (19-02-2021)

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Domaine public

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  • HAL Id : hal-03146682 , version 1

Citer

Jean-Louis Verger-Gaugry. Limit Conjectures in Number Theory, Lehmer's Conjecture, Conjecture of Schinzel-Zassenhaus, dynamical zeta function of the beta-shift: Part 1.-- Conjecture de Lehmer, Conjecture de Schinzel-Zassenhaus. Minoration of the Mahler measure, minoration of heights, problem of Lehmer. Analogues and generalizations, limit problems, Perron numbers, Pisot numbers, Salem numbers. Boyd's Conjectures on Salem numbers, Theorems of Boyd-Lawton and Doche. Mahler measure of multivariate polynomials. Cohomological interpretations: Deninger, Boyd, Rodriguez-Villegas. 2018. ⟨hal-03146682⟩
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