Related papers: Eisenstein integrals and induction of relations

We introduce an integral version of the Eisenstein cocycle. As applications we prove a conjecture of Gross regarding the "order of vanishing" of Stickelberger elements relative to an abelian tower of fields and give a cohomological…

The classical Hilbert specialization property is a field-theoretic tool ensuring that polynomial irreducibility over a field is preserved under specialization of some of the variables. We develop an integral counterpart by introducing the…

The starting point for this work is an identity that relates the number of minimal matrices with prescribed 1-marginals and coefficient sequence to a linear combination of Kronecker coefficients. In this paper we provide a bijection that…

We review the Kohno-Drinfeld theorem as well as a conjectural analogue relating quantum Weyl groups to the monodromy of a flat connection D on the Cartan subalgebra of a complex, semi-simple Lie algebra g with poles on the root hyperplanes…

In this paper, we consider a $q$-analogue of the Dunkl operator on $\mathbb{R}$, we define and study its associated Fourier transform which is a $q$-analogue of the Dunkl transform. In addition to several properties, we establish an…

Many concepts of Fourier analysis on Euclidean spaces rely on the specification of a frequency point. For example classical Littlewood Paley theory decomposes the spectrum of functions into annuli centered at the origin. In the presence of…

We consider a class of domains, generalizing the upper half-plane, and admitting rotational, translational and scaling symmetries, analogous to the half-plane. We prove Paley-Wiener type representations of functions in Bergman spaces of…

This paper provides a formula for the minimal relations and the Frobenius number of a numerical semigroup minimally generated by three pairwise coprime positive integers.

We study modular forms for the minimal index noncongruence subgroups of the modular group. Our main theorem is a proof of the unbounded denominator conjecture for these groups, and we also provide a study of the Fourier coefficients of…

In this paper, we first investigate the relationship between the number of primitive representations of $n$ by quadratic forms and the number of non-primitive ones. We hence obtain a theorem to deal with the Eisenstein series part with…

We prove exponential mixing for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations (Theorem 3)

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…

A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and…

We demonstrate the existence of minimal simplicial $n$-complexes which inevitably contain a nonsplittable two-component link formed by an $(n-1)$-sphere and an $n$-sphere in any embedding into $\mathbb{R}^{2n}$. This provides a…

A special class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions are analyzed via the inverse scattering method (ISM). Using the dressing method we construct two classes…

Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for constructing multivariate intersection numbers relevant to Feynman integrals,…

From the theory of modular forms, there are exactly $[(k-2)/6]$ linear relations among the Eisenstein series $E_k$ and its products $E_{2i}E_{k-2i}\ (2\le i \le [k/4])$. We present explicit formulas among these modular forms based on the…

We derive an integral formula for the linking number of two submanifolds of the n-sphere S^n, of the product S^n x R^m, and of other manifolds which appear as "nice" hypersurfaces in Euclidean space. The formulas are geometrically…

We provide a new foundation for combinatorial commutative algebra and Stanley-Reisner theory using the partition complex introduced in [Adi18]. One of the main advantages is that it is entirely self-contained, using only a minimal knowledge…

This paper presents a brief exposition of Soergel bimodules with applications to some topics in Kazhdan-Lusztig theory. We ultimately exposit a few of Soergel's main results, which allowed him to give alternative proofs, using his theory,…