On the refined Gan-Gross-Prasad conjecture for cusp forms of GSp(4)

We prove a conjectural formula relating the Bessel period of certain automorphic forms on $\mathrm{GSp}_4$ to a central $L$-value. This formula is proposed by Liu \cite{liu} as the refined Gan-Gross-Prasad conjecture for the groups (\SO(5), \SO(2)). The conjecture has been previously proved for certain automorphic forms on $\mathrm{GSp_4}$ from lifts. In this paper, we extend the formula to Siegel modular forms of \Sp_4(\bZ).Comment: fix constant 1/8; discuss the global L-function. arXiv admin note: text overlap with arXiv:1510.0733

Bhargava Integer Cubes and Weyl Group Multiple Dirichlet Series

We investigate the Shintani zeta functions associated to the prehomogeneous spaces, the example under consideration is the set of $2 \times 2\times 2$ integer cubes. We show that there are three relative invariants under a certain parabolic group action, they all have arithmetic nature and completely determine the equivalence classes. We show that the associated Shintani zeta function coincides with the $A_3$ Weyl group multiple Dirichlet series. Finally, we show that the set of semi-stable integer orbits maps finitely and surjectively to a certain moduli space

Bhargava's composition law and Waldspurger's central value theorem

We reprove a Waldspurger's formula which relates the toric periods and the central values of L-functions of GL2. Our technique, different from the original theta-correspondence approach and the more recent relative trace formula, relies on the exploit of distributions defined on prehomogeneous vector spaces.Comment: arXiv admin note: text overlap with arXiv:1311.213

Landau levels of cold dense quark matter in a strong magnetic field

The occupied Landau levels of strange quark matter are investigated in the framework of the SU(3) NJL model with a conventional coupling and a magnetic-field dependent coupling respectively. At lower density, the Landau levels are mainly dominated by u and d quarks. Threshold values of the chemical potential for the s quark onset are shown in the $\mu$-$B$ plane. The magnetic-field-dependent running coupling can broaden the region of three-flavor matter by decreasing the dynamical masses of $s$ quarks. Before the onset of $s$ quarks, the Landau level number of light quarks is directly dependent on the magnetic field strength $B$ by a simple inverse proportional relation $k_{i,\mathrm{max}}\approx B_i^0/B$ with $B_d^0=5\times 10^{19}$ G, which is approximately 2 times $B_u^0$ of $u$ quarks at a common chemical potential. When the magnetic field increases up to $B^0_d$, almost all three flavors are lying in the lowest Landau level.Comment: 8 pages, 6 figures, 1 table, arXiv admin note: text overlap with arXiv:1602.0393

Simulating the Chiral Magnetic Wave in a Box System

The chiral magnetic wave from the interplay between the chiral magnetic effect and the chiral separation effect is simulated in a box system with the periodic boundary condition based on the chiral kinetic equations of motion. Simulation results are compared with available limits from theoretical derivations, and effects of the temperature, the magnetic field, and the specific shear viscosity on the key properties of the chiral magnetic wave are discussed. Our study serves as a baseline for further simulations of chiral anomalies in relativistic heavy-ion collisions.Comment: 7 pages, 5 figure

Variational principle for weighted topological pressure

Let $\pi:X\to Y$ be a factor map, where $(X,T)$ and $(Y,S)$ are topological dynamical systems. Let ${\bf a}=(a_1,a_2)\in {\Bbb R}^2$ with $a_1>0$ and $a_2\geq 0$, and $f\in C(X)$. The ${\bf a}$-weighted topological pressure of $f$, denoted by $P^{\bf a}(X, f)$, is defined by resembling the Hausdorff dimension of subsets of self-affine carpets. We prove the following variational principle: $$P^{\bf a}(X, f)=\sup\left\{a_1h_\mu(T)+a_2h_{\mu\circ\pi^{-1}}(S)+\int f \;d\mu\right\},$$ where the supremum is taken over the $T$-invariant measures on $X$. It not only generalizes the variational principle of classical topological pressure, but also provides a topological extension of dimension theory of invariant sets and measures on the torus under affine diagonal endomorphisms. A higher dimensional version of the result is also established

Quantum Signature Protocol without the Trusted Third Party

An authentic digital signature scheme based on the correlation of Greenberger-Horne-Zeilinger (GHZ) states was presented. In this scheme, by performing a local unitary operation on the third particles of each GHZ triplet, Alice can encode message M and get its signature S. Bob performs CNOT operation on the combined GHZ triplets can recovery the message M and directly authenticates Alice's signature S. Our scheme was designed to use quantum secret key to guaranteed unconditional security, as well as use quantum fingerprinting to avoid trick attacks and reduce communication complexity.Comment: 5 page

Simulating chiral anomalies with spin dynamics

Considering that the chiral kinetic equations of motion (CEOM) can be derived from the spin kinetic equations of motion (SEOM) for massless particles with approximations, we simulate the chiral anomalies by using the latter in a box system with the periodic boundary condition under a uniform external magnetic field. We found that the chiral magnetic effect is weaker while the damping of the chiral magnetic wave is stronger from the SEOM compared with that from the CEOM. In addition, effects induced by chiral anomalies from the SEOM are less sensitive to the decay of the magnetic field than from the CEOM due to the spin relaxation process.Comment: 6 pages, 6 figure

Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation

Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function satisfying the globally log-H\"{o}lder continuous condition, $q\in(0,\infty]$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. In this article, the authors first introduce the anisotropic variable Hardy-Lorentz space $H_A^{p(\cdot),q}(\mathbb R^n)$ associated with $A$, via the radial grand maximal function, and then establish its radial or non-tangential maximal function characterizations. Moreover, the authors also obtain characterizations of $H_A^{p(\cdot),q}(\mathbb R^n)$, respectively, in terms of the atom and the Lusin area function. As an application, the authors prove that the anisotropic variable Hardy-Lorentz space $H_A^{p(\cdot),q}(\mathbb R^n)$ severs as the intermediate space between the anisotropic variable Hardy space $H_A^{p(\cdot)}(\mathbb R^n)$ and the space $L^\infty(\mathbb R^n)$ via the real interpolation. This, together with a special case of the real interpolation theorem of H. Kempka and J. Vyb\'iral on the variable Lorentz space, further implies the coincidence between $H_A^{p(\cdot),q}(\mathbb R^n)$ and the variable Lorentz space $L^{p(\cdot),q}(\mathbb R^n)$ when $\mathop\mathrm{essinf}_{x\in\mathbb{R}^n}p(x)\in (1,\infty)$.Comment: 42 pages, Submitte

Littlewood-Paley Characterizations of Anisotropic Hardy-Lorentz Spaces

Let $p\in(0,1]$, $q\in(0,\infty]$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. Let $H^{p,q}_A(\mathbb{R}^n)$ be the anisotropic Hardy-Lorentz spaces associated with $A$ defined via the non-tangential grand maximal function. In this article, the authors characterize $H^{p,q}_A(\mathbb{R}^n)$ in terms of the Lusin-area function, the Littlewood-Paley $g$-function or the Littlewood-Paley $g_\lambda^*$-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz space $L^{p,q}(\mathbb{R}^n)$. All these characterizations are new even for the classical isotropic Hardy-Lorentz spaces on $\mathbb{R}^n$. Moreover, the range of $\lambda$ in the $g_\lambda^*$-function characterization of $H^{p,q}_A(\mathbb{R}^n)$ coincides with the best known one in the classical Hardy space $H^p(\mathbb{R}^n)$ or in the anisotropic Hardy space $H^p_A(\mathbb{R}^n)$.Comment: 40 pages; Submitted. arXiv admin note: text overlap with arXiv:1512.0508