Related papers: Quadratic relations between Bessel moments

In the random-interaction ensembles, three proportional correlations between quadrupole moments of the first two $I^{\pi}=2^+$ states robustly emerge, including $Q(2^+_1)=\pm Q(2^+_2)$ correlations consistently with realistic nuclear…

Perturbative quantum field theory for the Ising model at the three-loop level yields a tetrahedral Feynman diagram C(a,b) with masses a and b and four other lines with unit mass. The completely symmetric tetrahedron C^Tet \equiv C(1,1) has…

A class of orthogonal polynomials associated with Coulomb wave functions is introduced. These polynomials play a role analogous to that the Lommel polynomials do in the theory of Bessel functions. The measure of orthogonality for this new…

Let $n=2m$. In the present paper, we study the binomial Boolean functions of the form $$f_{a,b}(x) = \mathrm{Tr}_1^{n}(a x^{2^m-1 }) +\mathrm{Tr}_1^{2}(bx^{\frac{2^n-1}{3} }), $$ where $m$ is an even positive integer, $a\in…

Let $f$ be a cuspidal eigenform of weight $k$ on $\SL_2(\BZ)$ and let $\lambda_{\Sym^d f}(n)$ be the normalized Fourier coefficients of its $d$-th symmetric power lift. This paper establishes asymptotic formulas for the moments $\sum_{n\leq…

We study the Fourier transform of polynomials in an orthogonal family, taken with respect to the orthogonality measure. Mastering the asymptotic properties of these transforms, that we call Fourier--Bessel functions, in the argument, the…

We develope the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic Hecke $L$-functions in the Gaussian field using multiple Dirichlet series under the generalized…

We prove a new upper bound on the second moment of Maass form symmetric square L-functions defined over Gaussian integers. Combining this estimate with the recent result of Balog-Biro-Cherubini-Laaksonen, we improve the error term in the…

Recently R.Khan and M.Young proved a mean Lindel\"{o}f estimate on the second moment of central values of Maass form symmetric-square $L$-function on the interval $T<|t_j|<T+T^{1/5+\epsilon}$, where $t_j$ is a spectral parameter of the…

We develop a novel numerical bootstrap for unitary, crossing-symmetric conformal field theories, focusing on moment observables defined as weighted averages over conformal data. Providing a global and coarse-grained probe of the operator…

This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\^o integrals with respect to the compensated Poisson process.…

We develop a new method for studying sums of Kloosterman sums related to the spectral exponential sum. As a corollary, we obtain a new proof of the estimate of Soundararajan and Young for the error term in the prime geodesic theorem.

In this paper, we study the moments of central values of Hecke $L$-functions associated with quadratic characters in $\mathbb{Q}(i)$ and $\mathbb{Q}(\omega)$ with $\omega = exp(2\pi i/3)$ and establish some quantitative non-vanishing result…

We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include…

We show that in Lorentzian manifolds, sectional curvature bounds of the form $\mathcal{R}\le K\,$, as defined by Andersson and Howard, are closely tied to space-time convex and $\lambda$-convex ($\lambda>0$) functions, as defined by Gibbons…

Let $L/K$ be a quadratic extension of global fields. We study Cohen-Lenstra heuristics for the $\ell$-part of the relative class group $G_{L/K} := \textrm{Cl}(L/K)$ when $K$ contains $\ell^n$th roots of unity. While the moments of a…

In terms of the Beltrami model of de Sitter space we show that there is an interchangeable relation between Snyder's quantized space-time model in dS-space of momenta at the Planck length $\ell_P=(G\hbar c^{-3})^{1/2}$ and the dS-invariant…

Based on an extended time-space symmetry, a cylindrical model of gravitational geometrical dynamics with two time-like extra-dimensions leads to a microscopic geodesic description of the curved space-time. Due to interaction of a Higgs-like…

In this paper, we construct four infinite families of ternary linear codes associated with double cosets in $O(2n+1,q)$ with respect to certain maximal parabolic subgroup of the special orthogonal group $SO(2n+1,q)$. Here $q$ is a power of…

We consider quantum symmetric algebras, FRT bialgebras and, more generally, intertwining algebras for pairs of Hecke symmetries which represent quantum hom-spaces. The paper makes an attempt to investigate Koszulness and Gorensteinness of…