BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Riccardo Pengo (École normale supérieure de Lyon) DTSTART:20220317T104500Z DTEND:20220317T114500Z DTSTAMP:20260423T035913Z UID:NTUniPD/2 DESCRIPTION:Title: Limits of Mahler measures and (successively) exact polynomials\nby Ric cardo Pengo (École normale supérieure de Lyon) as part of Number Theory Seminars at Università degli Studi di Padova\n\n\nAbstract\nMahler's meas ure is a height function of fundamental importance in Diophantine geometry \, protagonist of a celebrated problem posed by Lehmer. The work of Boyd h as shown that Lehmer's problem can be approached by studying Mahler measur es of multivariate polynomials\, and that the latter are often linked to s pecial values of $L$-functions. In this seminar\, I will talk about a gene ralization of the work of Boyd\, obtained jointly with François Brunault\ , Antonin Guilloux and Mahya Mehrabdollahei\, in which we find a class of sequences of polynomials whose Mahler measures converge. Furthermore\, we provide an explicit upper bound for the error term\, and an asymptotic exp ansion for a particular family of polynomials\, whose terms share all the peculiar property of being "exact". If time permits\, I will explain more in detail this notion of exactness\, and talk about a generalization of it (the notion of "successive exactness")\, studied jointly with François B runault\, which is related to a certain "weight loss" of the $L$-functions whose special values are conjecturally related to the Mahler measure of t he polynomial in question.\n LOCATION:https://researchseminars.org/talk/NTUniPD/2/ END:VEVENT END:VCALENDAR