Related papers: 2-Adic Stratification of Totients

Properties of 2-adic valuation sequences for general quadratic polynomials with integer coefficients are determined directly from the coefficients. These properties include boundedness or unboundedness, periodicity, and valuations at…

In this paper we study the distribution of totients $2$ mod. $4$. We prove that the asymptotic magnitude of such totients with multiplicity two is half of that of prime numbers. As a corollary we obtain that the relative asymptotic density…

The p-adic valuation of a polynomial can be given by its valuation tree. This work describes the 2-adic valuation tree of the general degree 2 polynomial in 2 variables.

This paper investigates the p-adic valuation trees of degree-2 and degree-3 polynomials in two variables over any prime p, building upon prior research outlined in [14].

The natural occurrence of singular spaces in applications has led to recent investigations on performing topological data analysis (TDA) in a stratified framework. In many applications, there is no a priori information on what points should…

This paper defines and studies a stratification of the adjoint quotient of the Lie algebra of a reductive group over a Laurent power series field. The stratification arises naturally in the context of affine Springer fibers.

In this paper we study the topology of the strata, indexed by number partitions $\lambda$, in the natural stratification of the space of monic hyperbolic polynomials of degree $n$. We prove stabilization theorems for removing an independent…

This is the second part of a two part paper. In this part, we evaluate the previously unevaluated local densities at dyadic places which appear in the density theorem stated in the first part. For this part, we introduce an invariant, the…

The article motivates, presents and describes large computer calculations concerning the asymptotic behaviour of arithmetic properties of coefficient fields of modular forms. The observations suggest certain patterns, which deserve further…

We give an intrinsic characterization of multisymplectic manifolds that have the linear type of density-valued symplectic forms in each tangent space, prove Darboux-type theorems for these forms, and investigate their symmetries.

In this paper, we extend Beta distribution to 2 by 2 matrix and give the analytical formula for its moments. Our analytical formula can be used to analyze the asymptotic behavior of Beta distribution for 2 by 2 matrix.

2-stratifolds are a generalization of 2-manifolds in that there are disjoint simple closed curves where several sheets meet. They arise in the study of categorical invariants of 3-manifolds and may have applications to topological data…

Let $(M,g)$ be a compact smoothly stratified pseudomanifold with an iterated cone-edge metric satisfying a spectral Witt condition. Under these assumptions the Hodge-Laplacian $\Delta$ is essentially self-adjoint. We establish the…

We investigate average gradient degree of normal random polynomials of fixed algebraic degree n. In particular, for polynomials of two variables, asymptotics of the average gradient degree for large values of n is determined.

This article is concerned with the asymptotic behavior of the two-dimensional inviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time-decay rates of the smooth solutions to that system. The…

We determine the number of ergodic measures in each stratum of geodesic laminations on a surface.

This paper studies a two-stage model of experimentation, where the researcher first samples representative units from an eligible pool, then assigns each sampled unit to treatment or control. To implement balanced sampling and assignment,…

In this paper we compute the 2-adic valuations of some polynomials associated with the definite integral $\int_{0}^{\infty} \frac{dx}{(x^4+2*a*x^2+1)^(m+1)}$

We investigate the asympotic behaviour of the moduli space of morphisms from the rational curve to a given variety when the degree becomes large. One of the crucial tools is the homogeneous coordinate ring of the variey. First we explain in…

We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two research topics that have been very active recently:…