Related papers: Dwork congruences via q-deformation

We prove that the algebra of functions on the cotangent bundle $T^*(G/U_P)$ of the parabolic base affine space for a reductive group $G$ and a parabolic subgroup $P$ is isomorphic to the subalgebra of the functions on $G \times L \times…

Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…

Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D4,E6,E7,E8). To such a diagram one can attach a group G whose generators correspond to the legs of the affinization, have orders equal to…

We consider q-deformations of Witt rings, based on geometric operations on zeta functions of motives over finite fields, and we use these deformations to construct q-analogs of the Bost-Connes quantum statistical mechanical system. We show…

We define and study a series indexed by rooted trees and with coefficients in Q(q). We show that it is related to a family of Lie idempotents. We prove that this series is a q-deformation of a more classical series and that some of its…

Gaussian polynomial, which is also known as $q$-binomial coefficient, is one of the fundamental concepts in the theory of partitions. Zeilberger provided a combinatorial proof of Gaussian polynomial, which is called Algorithm Z by Andrews…

We show that the coefficients of the power series expansion of the principal period of a Laurent polynomial satisfy strong congruence properties. These congruences play a key role in the explicit p-adic analytic continuation of the unit…

In this paper, the $(p,q)$-derivative and the $(p,q)$-integration are investigated. Two suitable polynomials bases for the $(p,q)$-derivative are provided and various properties of these bases are given. As application, two $(p,q)$-Taylor…

The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling…

Fulton's universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear…

We characterise the quantum group gauge symmetries underlying q-deformations of two-dimensional Yang-Mills theory by studying their relationships with the matrix models that appear in Chern-Simons theory and six-dimensional N=2 gauge…

Okuyama introduced a family of polynomials, whose coefficients depend on a parameter $q$, in his study of correlators in the double-scaled SYK model. He verified in small cases that their coefficients can be expressed in terms of certain…

The aim of this work is to establish congruences $\left( \operatorname{mod}p^{2}\right) $ involving the trinomial coefficients $\binom{np-1}{p-1}_{2}$ and $\binom{np-1}{\left( p-1\right)/2}_{2}$ arising from the expansion of the powers of…

q-Deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is discussed by using an extension of the number concept proposed by Gauss, namely the Q-numbers. A study of the reducibility of the Fock…

We investigate the "$T\bar{T}$" deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the $T\bar{T}$ deforming operator can…

It is well-known that Hodge numbers are invariant under deformations of complex structures if the Fr\"olicher spectral sequence of the central fiber degenerates at the first page (i.e. $E_1=E_\infty$). As a result, the deformations of…

We derive the $T\overline{T}$-perturbed version of two-dimensional $q$-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the…

We prove a structural result for degree-$d$ polynomials. In particular, we show that any degree-$d$ polynomial, $p$ can be approximated by another polynomial, $p_0$, which can be decomposed as some function of polynomials $q_1,...,q_m$ with…

The topological Tverberg theorem claims that for any continuous map of the (q-1)(d+1)-simplex to R^d there are q disjoint faces such that their images have a non-empty intersection. This has been proved for affine maps, and if $q$ is a…

We introduce a basis of rational polynomial-like functions $P_0,\ldots,P_{n-1}$ for the free module of functions $Z/nZ\to Z/mZ$. We then characterize the subfamily of congruence preserving functions as the set of linear combinations of the…