Related papers: A recursion for a symmetric function generalizatio…

The Constant Degree Hypothesis was introduced by Barrington et. al. (1990) to study some extensions of $q$-groups by nilpotent groups and the power of these groups in a certain computational model. In its simplest formulation, it…

We prove a conjecture of Viterbo from 2007 on the existence of a uniform bound on the Lagrangian spectral norm of Hamiltonian deformations of the zero section in unit cotangent disk bundles, for bases given by compact rank one symmetric…

In 1995 Magnus posed a conjecture about the asymptotics of the recurrence coefficients of orthogonal polynomials with respect to the weights on [-1,1] of the form $$ (1-x)^\alpha (1+x)^\beta |x_0 - x|^\gamma \times a jump at x_0, $$ with…

In math.CO/0109093 the author obtained a formula for the value of an irreducible symmetric group character indexed by a partition of rectangular shape. In the present paper this formula is (conjecturally) generalized to arbitrary shapes.

In statistical physics, the Nakajima-Mori-Zwanzig projection operator formalism is used to derive an integro-differential equation for observables in a Hilbert space, the generalized Langevin equation (GLE). This technique relies on the…

In 1975 Voronin proved the universality theorem for the Riemann zeta-function $\zeta(s)$ which roughly says that any admissible function $f(s)$ is approximated by $\zeta(s)$. A few years later Reich proved a discrete analogue of this…

We prove the inhomogeneous generalization of the Duffin-Schaeffer conjecture in dimension $m \geq 3$. That is, given $\mathbf{y}\in \mathbb{R}^m$ and $\psi:\mathbb{N}\to\mathbb{R}_{\geq 0}$ such that $\sum (\varphi(q)\psi(q)/q)^m = \infty$,…

We consider a class of ordinary differential equations describing one-dimensional analytic systems with a quasi-periodic forcing term and in the presence of damping. In the limit of large damping, under some generic non-degeneracy condition…

The objective of this article is to prove the necessity statement in Crawley-Boevey's conjectural solution to the (tame) Deligne-Simpson problem. We use the nonabelian Hodge correspondence, variation of parabolic weights and results of…

It is shown that the q-difference Noether problem for all classical Weyl groups has a positive solution, simultaneously generalizing well known results on multisymmetric functions of Mattuck and Miyata in the case q=1, and q-deforming the…

The Lebesgue dominated convergence theorem of the measure theory implies that the Riemann integral of a bounded sequence of continuous functions over the interval [ 0,1] pointwise converging to zero, also converges to zero. The validity of…

An important family of structural constants in the theory of symmetric functions and in the representation theory of symmetric groups and general linear groups are the plethysm coefficients. In 1950, Foulkes observed that they have some…

The classical Bott-Samelson theorem states that if on a Riemannian manifold all geodesics issuing from a certain point return to this point, then the universal cover of the manifold has the cohomology ring of a compact rank one symmetric…

A classical result due to Levinson characterizes the existence of non-zero functions defined on a circle vanishing on an open subset of the circle in terms of the pointwise decay of their Fourier coefficients [13]. We prove certain analogue…

We show that the sign constancy for the values of certain weighted summatory functions of the von Mangoldt function implies the Riemann hypothesis or the generalized Riemann hypothesis for Dirichlet $L$-functions. While such sign constancy…

We introduce a quasisymmetric class function associated with a group acting on a double poset or on a directed graph. The latter is a generalization of the chromatic quasisymmetric function of a digraph introduced by Ellzey, while the…

Generalized smooth functions are a possible formalization of the original historical approach followed by Cauchy, Poisson, Kirchhoff, Helmholtz, Kelvin, Heaviside, and Dirac to deal with generalized functions. They are set-theoretical…

Let $\mathcal{S}$ denote the class of analytic and univalent ({\it i.e.}, one-to-one) functions $f(z)= z+\sum_{n=2}^{\infty}a_n z^n$ in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$. For $f\in \mathcal{S}$, Ma proposed the…

Morrey Conjecture deals with two properties of functions which are known as quasi-convexity and rank-one convexity. It is well established that every function satisfying the quasi-convexity property also satisfies rank-one convexity. Morrey…

A generalization of Young's inequality for convolution with sharp constant is conjectured for scenarios where more than two functions are being convolved, and it is proven for certain parameter ranges. The conjecture would provide a unified…