arXiv subjects

Thomas Mégarbané

Publications and source records attributed to Thomas Mégarbané.

3 recordsLinked to original sources

arXiv2016

Calcul des opérateurs de Hecke sur les classes d'isomorphisme de réseaux pairs de déterminant 2 en dimension 23 et 25

In this article, we compute the Hecke operator $\mathrm{T}_2$, associated to the Kneser $2$-neighbours, defined on the isomorphic classes of even lattices of determinant 2, in dimension 23 and 25. In a previous article, we computed some properties of the Satake parameters of the automorphic representations for the linear groups discovered by Chenevier and Renard. Thanks to these results, we deduce the value of many other Hecke operators. This enables us to compute for every prime $p$ the Kneser graph associated to the $p$-neighbours of lattices in dimension 23 and 25. From our results, we improve Harder's conjecture, and also prove many other congruences involving the Satake parameters of the automorphic representations for the linear groups discovered by Chenevier and Renard.

math.NT↗

arXiv2016

Eisenstein congruences for SO(4,3), SO(4,4), spinor and triple product L-values

We work out instances of a general conjecture on congruences between Hecke eigenvalues of induced and cuspidal automorphic representations of a reductive group, modulo divisors of certain critical L-values, in the case that the group is a split orthogonal group. We provide some numerical evidence in the case that the group is SO(4,3) and the L-function is the spinor L-function of a genus 2, vector-valued, Siegel cusp form. We also consider the case that the group is SO(4,4) and the L-function is a triple product L-function.

math.NT↗

arXiv2016

Traces des opérateurs de Hecke sur les espaces de formes automorphes de $\mathrm{SO}_7$, $\mathrm{SO}_8$ ou $\mathrm{SO}_9$ en niveau $1$ et poids arbitraire

In this article, we determine the trace of some Hecke operators on the spaces of level one automorphic forms on the special orthogonal groups of the euclidean lattices $\mathrm{E}_7$, $\mathrm{E}_8$ and $\mathrm{E}_8\oplus \mathrm{A}_1$, with arbitrary weight. Using Arthur's theory, we deduce properties of the Satake parameters of the automorphic representations for the linear groups discovered by Chenevier and Renard. Our results corroborate a conjecture by Bergström, Faber and van der Geer about the Hasse-Weil zeta function on the moduli spaces of $17$-pointed curves of genus $3$.

math.NT↗