Related papers: Linear independence measures for Chowla--Selberg p…
In the present work we consider a time-dependent Schr\"odinger equation for systems invariant under the reparametrization of time. We develop the two-stage procedure of construction such systems from a given initial ones, which is not…
For a general dyadic grid, we give a Calder\'{o}n-Zygmund type decomposition, which is the principle fact about the multilinear maximal function $\mathfrak{M}$ on the upper half-spaces. Using the decomposition, we study the boundedness of…
It was recently proposed that there is a phase in thermal QCD (IR phase) at temperatures well above the chiral crossover, featuring elements of scale invariance in the infrared (IR). Here we study the effective spatial dimensions, $d_{IR}$,…
To quantify degree of spatial inhomogeneity for multiphase materials we adapt the entropic descriptor (ED) of a pillar model developed to greyscale images. To uncover the contribution of each phase we introduce the suitable 'phase…
In this article we obtain new irrationality measures for values of functions which belong to a certain class of hypergeometric functions including shifted logarithmic functions, binomial functions and shifted exponential functions. We…
We give the exact expressions of the partial susceptibilities $\chi^{(3)}_d$ and $\chi^{(4)}_d$ for the diagonal susceptibility of the Ising model in terms of modular forms and Calabi-Yau ODEs, and more specifically, $_3F_2([1/3,2/3,3/2],\,…
The Schur index is a powerful tool to probe the spectrum and dualities of 4d $\mathcal{N}=2$ superconformal field theories (SCFTs), deeply related to 2d vertex operator algebras (VOAs). In this paper, we compute the Schur index in closed…
We consider parameter estimation for a linear parabolic second-order stochastic partial differential equation (SPDE) in two space dimensions driven by two types $Q$-Wiener processes based on high frequency data in time and space. We first…
We discuss a one-dimensional version of the Landau-Pekar equations, which are a system of coupled differential equations with two different time scales. We derive an approximation on the slow time scale in the spirit of a non-linear…
The 3D Bondi-Metzner-Sachs (BMS$_3$) algebra that is the asymptotic symmetry algebra at null infinity of the $1+2$D asymptotically flat space-time is isomorphic to the $1+1$D Carrollian conformal algebra. Building on this connection,…
The study of linear independence of $L(k, \chi)$ for a fixed integer $k>1$ and varying $\chi$ depends critically on the parity of $k$ vis-\`a-vis $\chi$. This has been investigated by a number of authors for Dirichlet characters $\chi$ of a…
In this article, we describe a simple covariant characterisation of initial data sets which give rise to Petrov type D vacuum spacetime developments. As an application, we derive an integral invariant which, when restricted to the…
We investigate the asymptotic behaviour of nonlinear Schr\"odinger ground states on $d$-dimensional periodic metric grids in the limit for the length of the edges going to zero. We prove that suitable piecewise-affine extensions of such…
Given a positive increasing function $\varphi$, we show that for a full measure set of vectors $\alpha\in \mathbb{R}^d$, the maximal ergodic discrepancy of the $d$-linear form sequence $\left\{\sum_{1\le i\le d} k_i\alpha_i \mod…
We perform numerical simulations of the critical gravitational collapse of a spherically symmetric scalar field in 6 dimensions. The critical solution has discrete self-similarity. We find the critical exponent \gamma and the…
We study the restriction of the Bump-Friedberg integrals to affine lines $\{(s+\alpha,2s),s\in\C\}$. It has a simple theory, very close to that of the Asai $L$-function. It is an integral representation of the product…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
\begin{abstract} In this article, we will get non-trivial estimates for the central values of degree six Rankin-Selberg $L$-functions $L(1/2+it, \pi \times f)$ associated with a ${GL(3)}$ form $\pi$ and a ${GL(2)} $ form $f$ using the delta…
Let $E/F$ be a quadratic extension of $p$-adic fields and let $d$, $m$ be nonnegative integers of distinct parities. Fix admissible irreducible tempered representations $\pi$ and $\sigma$ of $GL_d(E)$ and $GL_m(E)$ respectively. We assume…
For coupled-dimer Heisenberg magnets, a paradigm of magnetic quantum phase transitions, we develop a systematic expansion in 1/d, the inverse number of space dimensions. The expansion employs a formulation of the bond-operator technique and…