Taking t at random, uniformly from [0,T], we consider the kth moment, with respect to t, of random variable corresponding 2?th moment ?(1/2+ix) over interval x?(t,t+1], where ?(s) is Riemann zeta function. We call these ‘moments moments’ function, and present a conjecture for their asymptotics, when T??, integer k,?. This motivated by comparisons results moments characteristic polynomials unita...

In 1972, H.L. Montgomery and F. Dyson uncovered a surprising connection between the Theory of the Riemann Zeta function and Random Matrix Theory. For the next few decades, the major developments in the area were the numerical calculations of Odlyzko and conjectures for the moments of the Riemann Zeta function (and other L-functions) found by Conrey, Ghosh, Gonek, Heath-Brown, Hejhal and Sarnak....

The central moments of the multivariate normal distribution are functions of its n×n variance-covariance matrix Σ. These moments can be expressed symbolically as linear combinations of products of powers of the elements of Σ. A formula for these moments derived by differentiating the characteristic function is developed. The formula requires searching integer matrices for matrices whose n succe...

We present a detailed analysis of resonance contributions in the context of higher twist effects in the moments of the proton spin structure function g 1. For each of these moments, it is found that there exists a characteristic Q 2 region in which (perturbative) higher twist corrections coexist with (non-perturbative) resonance contribution of comparable magnitude.

Here we consider a generalized log-transformed version of the Weibull distribution and investigate some its important properties like expressions for cumulative function hazard rate function, quantile characteristic raw moments, incomplete etc. The moments order statistics are obtained along with results on certain structural distribution. maximum likelihood estimation parameters is attempted b...

Statistical methods classically used to analyse a probability density function (pdf) are founded on the Fourier transform, on which useful tools such the first and second characteristic function are based, yielding the definitions of moments and cumulants. Yet this transformation is badly adapted to the analysis of probability density functions defined on R+, for which the analytic expressions ...

We use the analytical model recently introduced in Ref. [1], to investigate the statistics of temperature fluctuations on the cosmic microwave background (CMB), induced by topological defects. The cases of cosmic strings and textures are studied. We derive analytically the characteristic function of the probability distribution for δT T and use it to obtain the lowest twelve moments including t...