相关论文: Second moment of the light-cone Siegel transform a…
This paper revisits the quantum mechanics for one photon from the modern viewpoint and by the geometrical method. Especially, besides the ordinary (rectangular) momentum representation, we provide an explicit derivation for the other two…
This work studies the experiments of two-photon processes at BESIII from a theoretical viewpoint in light-cone quantum field theory. We adopt the momentum space wave function of the pion in the light-cone formalism by two forms of the…
We prove that the fourth moment of holomorphic Hecke cusp forms is bounded provided that the Riemann Hypothesis holds for an appropriate degree 8 L-function. We accomplish this using Watson's formula, which translates the question in hand…
Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has…
The generalisation of continuous orthogonal polynomial ensembles from random matrix theory to the $q$-lattice setting is considered. We take up the task of initiating a systematic study of the corresponding moments of the density from two…
Let $ \mathfrak{f} $ run over the space $ H_{4k} $ of primitive cusp forms of level one and weight $ 4k $, $ k \in N $. We prove an explicit formula for the mixed moment of the Hecke $ L $-function $ L(\mathfrak{f}, 1/2) $ and the symmetric…
In this work, we investigate the semi-leptonic weak decays of spin-1/2 doubly-heavy baryons $\Xi_{QQ^{\prime}}$ into spin-3/2 singly-heavy baryons $\Sigma_{Q^{\prime}}^*$ within light-cone sum rules. Using the parallel components of the…
In this note, we prove the existence of a secondary term in the asymptotic formula of the cubic moment of quadratic Dirichlet L-functions $$\sum_{\substack{d - \mathrm{monic \, \& \, sq. \, free} \mathrm{deg}\, d \, = \, D}}…
In this paper, we first construct generalized $q^2$-cosine, $q^2$-sine and $q^2$-exponential functions. We then use $q^2$-exponential function in order to define and investigate a $q^2$-Fourier transform. We establish $q$-analogues of…
The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or…
In this paper, let $f$ be a Hecke cusp form for $SL(2,\mathbb{Z})$. We establish an asymptotic formula for the mixed moment of $\zeta^{2}(s)$ and $L(s,f)$ on the critical line, valid for both holomorphic and Maass forms.
We use distribution amplitudes of the light $\Sigma$ baryon and the most general form of the interpolating current for heavy $\Sigma_b$ baryon to investigate the semileptonic $\Sigma_b\rightarrow \Sigma l^+l^-$ transition in light cone QCD…
Geometric moments and moment invariants of image artifacts have many uses in computer vision applications, e.g. shape classification or object position and orientation. Higher order moments are of interest to provide additional feature…
Conditionally on the Riemann Hypothesis we obtain bounds of the correct order of magnitude for the 2k-th moment of the Riemann zeta-function for all positive real k < 2.181. This provides for the first time an upper bound of the correct…
The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and…
We derive formulas for the terms in the conjectured asymptotic expansions of the moments, at the central point, of quadratic Dirichlet $L$-functions, $L(1/2,\chi_d)$, and also of the $L$-functions associated to quadratic twists of an…
We theoretically investigate the absorption and emission of light carrying orbital angular momentum (twisted-light) by quasi-two-dimensional (disc-shaped) quantum dots in the presence of a static magnetic field. We calculate the transition…
In this paper, we consider the $L$-functions $L(s, f)$ where $f$ is an eigenform for the congruence subgroup $\Gamma_1(q)$. We prove an asymptotic formula for the sixth moment of this family of automorphic $L$-functions.
This paper is mainly devoted to the determination of the travel time of a photon as a function of the positions of the emitter and the receiver in a large class of static, spherically symmetric spacetimes. Such a function - often called…
The analysis of $1/m_Q^2$ corrections of the previous paper is extended to the semileptonic decays of heavy baryons. We focus on the simplest case, the ground state $\Lambda_Q$ baryons, in which the light degrees of freedom are in a state…