Vlad Serban | EPFL Graph Search

À propos de ce résultat

Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.

Dense Packings via Lifts of Codes to Division Rings

Nihar Prakash Gargava, Vlad Serban

obtain algorithmically effective versions of the dense lattice sphere packings constructed from orders in Q-division rings by the first author. The lattices in question are lifts of suitable codes from prime characteristic to orders O in Q-division rings and we prove a Minkowski-Hlawka type result for such lifts. Exploiting the additional symmetries under finite subgroups of units in O, we show that this leads to effective constructions of lattices approaching the best known lower bounds on the packing density ?(n) in a variety of new dimensions n. This unifies and extends a number of previous constructions.

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

Unlikely intersections on the p-adic formal ball

Vlad Serban

We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a closed subscheme X -> F, we show under suitable assumptions that for any points P is an element of X(Cp) satisfying nP. is an element of(sic) for some n is an element of N, the minimal such orders n are uniformly bounded whenever X does not contain a formal subgroup translate of positive dimension. In contrast, we then provide counter-examples to a full p-adic formal Mordell-Lang result. Finally, we outline some consequences for the study of the Zariski-density of sets of automorphic objects in p-adic deformations. Specifically, we do so in the context of the nearly ordinary p-adic families of cuspidal cohomological automorphic forms for the general linear group constructed by Hida.

SPRINGER INT PUBL AG2023

A finiteness result for p-adic families of Bianchi modular forms

Vlad Serban

We study p-adic families of cohomological automorphic forms for GL(2) over imaginary quadratic fields and prove that families interpolating a Zariski-dense set of classical cuspidal automorphic forms only occur under very restrictive conditions. We show how to computationally determine when this is not the case and establish concrete examples of families interpolating only finitely many Bianchi modular forms. (C)& 2021 Elsevier Inc. All rights reserved.

ACADEMIC PRESS INC ELSEVIER SCIENCE2022