In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients. In [18], we proved that ...
We define and study in terms of integral Iwahoriâ Hecke algebras a new class of geometric operators acting on the Bruhat-Tits building of connected reductive groups over p-adic fields. These operators, which we call U-operators, generalize the geometric n ...
We apply the spectral curve topological recursion to Dubrovin's universal Landau-Ginzburg superpotential associated to a semi-simple point of any conformal Frobenius manifold. We show that under some conditions the expansion of the correlation differential ...
A classical result of Hasse states that the norm principle holds for finite cyclic extensions of global fields, in other words local norms are global norms. We investigate the norm principle for finite dimensional commutative kale algebras over global fiel ...
We present a self-contained proof of the following famous extension theorem due to Carl Herz. A closed subgroup H of a locally compact group G is a set of p-synthesis in G if and only if, for every u is an element of A(p)(H) boolean AND C-00(H) and for eve ...
Given a topological modular functor V in the sense of Walker, we construct vector bundles Z (lambda) over bar, over (M) over bar (g,n) whose Chern characters define semi-simple cohomological field theories. This construction depends on a determinati ...
We use Masser's counting theorem to prove a lower bound for the canonical height in powers of elliptic curves. We also prove the Galois case of the elliptic Lehmer problem, combining Kummer theory and Masser's result with bounds on the rank and torsion of ...
Embeddings of maximal tori in classical groups over fields of characteristic not 2 are the subject matter of several recent papers. The aim of the present paper is to give necessary and sufficient conditions for such an embedding to exist, when the base fi ...
For~q a prime power, the discrete logarithm problem (DLP) in~\Fq consists in finding, for any g∈Fq× and h∈⟨g⟩, an integer~x such that gx=h. We present an algorithm for computing discrete logarithm ...
Motivated by recent experimental progress in the context of ultra-cold multi-colour fermionic atoms in optical lattices, this thesis investigates the properties of the antiferromagnetic SU(N) Heisenberg models with fully antisymmetric irreducible represent ...
Let K be a global field of characteristic not 2. The embedding problem for maximal tori in a classical group G can be described in terms of algebras with involution. The aim of this paper is to give an explicit description of the obstruction group to the H ...
Let k be a global field of characteristic not 2, and let f is an element of k[X] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the compl ...
In this paper, we define Euclidean minima for function fields and give some bound for this invariant. We furthermore show that the results are analogous to those obtained in the number field case. (C) 2013 The Authors. Published by Elsevier Inc. All rights ...
We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic not equal 2 to contain a maximal torus of a given type. ...
We construct a bipartite Euler system in the sense of Howard for Hilbert modular eigenforms of parallel weight two over totally real fields, generalizing works of Bertolini-Darmon, Longo, Nekovar, Pollack-Weston, and others. The construction has direct app ...
The aim of this paper is to give upper bounds for the Euclidean minima of abelian fields of odd prime power conductor. In particular, these bounds imply Minkowski's conjecture for totally real number fields of conductor p(r), where p is an odd prime number ...
We establish several results towards the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication over imaginary quadratic fields, namely (i) the existence of an appropriate p-adic L-function, building on works of H ...
This thesis is concerned with the algebraic theory of hermitian forms. It is organized in two parts. The first, consisting of the first two chapters, deals with some descent properties of unimodular hermitian forms over central simple algebras with involut ...
We study annihilating polynomials and annihilating ideals for elements of Witt rings for groups of exponent 2. With the help of these results and certain calculations involving the Clifford invariant, we are able to give full sets of generators for the ann ...
Let F/E be a finite Galois extension of fields with abelian Galois group Γ. A self-dual normal basis for F/E is a normal basis with the additional property that TrF/E(g(x),h(x))=δg,h for g,h∈Γ. Bayer-Fluckiger and Lenstra h ...
