Related papers: Augmentation du niveau pour U(3) (Level-Raising fo…

For each integer $\ell \geq 1$, we prove an unconditional upper bound on the size of the $\ell$-torsion subgroup of the class group, which holds for all but a zero-density set of field extensions of $\mathbb{Q}$ of degree $d$, for any fixed…

Let $p$ be a prime number. We study the slopes of $U_p$-eigenvalues on the subspace of modular forms that can be transferred to a definite quaternion algebra. We give a sharp lower bound of the corresponding Newton polygon. The computation…

We establish the existence of de Rham lifts of Langlands parameters (or Galois representations) for unitary, orthogonal and symplectic (similitude) groups of arbitrary rank. Our results are unconditional except for the assumption $p>2$.

Isotopic liftings of algebraic structures are investigated in the context of Clifford algebras, where it is defined a new product involving an arbitrary, but fixed, element of the Clifford algebra. This element acts as the unit with respect…

We write the partition function for a lattice gauge theory, with compact gauge group, exactly in terms of unconstrained variables and show that, in the mean field approximation, the dynamics of pure gauge theories, invariant under compact,…

We present an explicit basis for orders of arbitrary level N>1 in definite rational quaternion algebras. These orders have applications to computations of spaces of elliptic and quaternionic modular forms.

We obtain a sharp refinement of the strong multiplicity one theorem for the case of unitary non-dihedral cuspidal automorphic representations for GL(2). Given two unitary cuspidal automorphic representations for GL(2) that are not…

The main objective of the present paper is to establish a new uncertainty principle (UP) for the two-sided quaternion Fourier transform (QFT). This result is an extension of a result of Benedicks, Amrein and Berthier, which states that a…

The Borcherds lift for indefinite unitary groups, previously constructed by the author, is examined here in greater detail for the special case of the group U(1,1). The inputs for the lifting in this case are weakly holomorphic modular…

We describe an algorithm to rigorously compute the power series expansion at a CM point of a weight $2$ cusp form of level coprime to $6$. Our algorithm works by bounding the denominators that appear due to ramification, and without…

We define algebras of quasi-quaternion type, which are symmetric algebras of tame representation type whose stable module category has certain structure similar to that of the algebras of quaternion type introduced by Erdmann. We observe…

We study the motivic cohomology of the special fiber of quaternionic Shimura varieties at a prime of good reduction. We exhibit classes in these motivic cohomology groups and use this to give an explicit geometric realization of level…

We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…

In arXiv:0905.1675, Nik Weaver proposed a novel intuitionistic formal theory of third-order arithmetic as a formalisation of his philosophical position known as mathematical conceptualism. In this paper, we will construct a realisability…

We discuss lifting properties of continuous homomorphisms from absolute Galois groups into (pro)finite groups. An analogy with the Langlands program is pointed out in the beginning of the note.

In this paper, we prove some computational results about equivariant cohomology over the cyclic group $C_{p^n}$ of prime power order. We show that there is an inductive formula when the dimension of the $C_p$-fixed points of the grading is…

This paper studies the Fourier expansion of Hecke-Maass eigenforms for $GL(2, \mathbb Q)$ of arbitrary weight, level, and character at various cusps. Translating well known results in the theory of adelic automorphic representations into…

Given a finite rank free group $\mathbb{F}$ of $\mathsf{rank}(\mathbb{F})\geq 3$, we show that the mapping torus of $\phi$ is (strongly) relatively hyperbolic if $\phi$ is exponentially growing. We combine our result with the work of…

This paper establishes an extended representation theorem for unit-root VARs. A specific algebraic technique is devised to recover stationarity from the solution of the model in the form of a cointegrating transformation. Closed forms of…

We show that complex multiplication on abelian varieties is equivalent to the existence of a constant rational K\"ahler metric. We give a sufficient condition for a mirror of an abelian variety of CM-type to be of CM-type as well. We also…