Related papers: $\zeta$-Pade SRWS theory with lowest order approxi…

This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…

We present Zeroth-order Riemannian Averaging Stochastic Approximation (\texttt{Zo-RASA}) algorithms for stochastic optimization on Riemannian manifolds. We show that \texttt{Zo-RASA} achieves optimal sample complexities for generating…

We present a method derived by cavity arguments to compute the spin-glass and higher-order susceptibilities in diluted mean-field spin-glass models. The divergence of the spin-glass susceptibility is associated to the existence of a…

Previously developed Pade-related method of resummation for QCD observables, which achieves exact renormalization-scale-invariance, is extended so that the scheme-invariance is obtained as well. The dependence on the leading scheme…

We show that the Green's function of a two dimensional fermion with a modified dispersion relation and short distance parameter $a$ is given by the Lerch zeta function. The Green's function is defined on a cylinder of radius R and we show…

Critical point scaling in a field $H$ applies for the limits $t\to 0$, (where $t=T/T_c-1$) and $H\to 0$ but with the ratio $R=t/H^{2/\Delta}$ finite. $\Delta$ is a critical exponent of the zero-field transition. We study the replicon…

Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…

The lattice Green function, i.e., the resolvent of the discrete Laplace operator, is fundamental in probability theory and mathematical physics. We derive its long-distance behaviour via a detailed analysis of an integral representation…

We obtain order estimates for the best uniform orthogonal trigonometric approximations of $2\pi$-periodic functions, whose $(\psi,\beta)$-derivatives belong to unit balls of spaces $L_{p}, \ 1\leq p<\infty$, in case at consequences…

Critical slowing down of the relaxation of the order parameter is relevant both in early the universe and in ultrarelativistic heavy ion collisions. We study the relaxation rate of the order parameter in an O(N) scalar theory near the…

We develop an $e_g$ orbital, $t$-$J$-like model of a single charge doped into a two-dimensional plane with ferromagnetic spin order and alternating orbital order, and present its solution by Green's functions in the variational…

We examine the two-point correlation functions of the fields exp(i$\alpha\Phi$) in the sine-Gordon theory at all values of the coupling constant $\hat\beta$. Using conformal perturbation theory, we write down explicit integral expressions…

We develop a concise self-consistent perturbation expansion for superconductivity where all the pair processes are naturally incorporated without drawing "anomalous" Feynman diagrams. This simplification results from introducing an…

We study the discretization of a linear evolution partial differential equation when its Green function is known. We provide error estimates both for the spatial approximation and for the time stepping approximation. We show that, in fact,…

The critical behavior of d-dimensional systems with an n-component order parameter is reconsidered at (m,d,n)-Lifshitz points, where a wave-vector instability occurs in an m-dimensional subspace of ${\mathbb R}^d$. Our aim is to sort out…

We show that the short-time critical exponent $\theta$ related to the critical initial slip in a stochastic model can be determined by the time correlation of the order parameter. In our procedure it suffices to start with an uncorrelated…

Four propositions are considered concerning the relationship between the zeros of two combinations of the Riemann zeta function and the function itself. The first is the Riemann hypothesis, while the second relates to the zeros of a…

We calculate the critical exponent $\eta$ of the $D$-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction. Our approach relies on the…

We report a numerical analysis of corrections to finite size scaling at the Anderson transition due to irrelevant scaling variables and non-linearities of the scaling variables. By taking proper account of these corrections, the…

To date the most precise estimations of the critical exponent for the Anderson transition have been made using the transfer matrix method. This method involves the simulation of extremely long quasi one-dimensional systems. The method is…