Let Pc(x)={p?x|p,[pc]areprimes},c?R+?N and ?sym2f(n) be the n-th Fourier coefficient associated with symmetric square L-function L(s,sym2f). For any A>0, we prove that mean value of over Pc(x) is ?xlog?A?2x for almost all c??,(5+3)/8?? in sense Lebesgue measure. Furthermore, it holds c?(0,1) under Riemann Hypothesis. obtain asymptotic formula ?f2(n) ?p,qprimep?x,q=[pc]?f2(p)=xclog2x(1+o(1)),...

The pseudodeterminant pdet(M) of a square matrix is the last nonzero coefficient in its characteristic polynomial; for a nonsingular matrix, this is just the determinant. If ∂ is a symmetric or skewsymmetric matrix then pdet(∂∂t) = pdet(∂)2. Whenever ∂ is the kth boundary map of a self-dual CWcomplex X, this linear-algebraic identity implies that the torsion-weighted generating function for cel...

This paper addresses the QR decomposition and UD factorization based square-root algorithms of the recursive least-squares (RLS) Wiener fixed-point smoother and filter. In the RLS Wiener estimators, the Riccati-type difference equations for the auto-variance function of the filtering estimate are included. Hence, by the roundoff errors, in the case of the small value of the observation noise va...

In this paper we prove results relating the (parabolic) non-tangential maximum operator and appropriate square functions in Lp for solutions to general second order, symmetric and strongly elliptic parabolic systems with real valued and constant coefficients in the setting of a class of time-varying, non-smooth infinite cylinders Ω. In particular we prove a global as well as a local and scale i...

In this paper we investigate non-central elements of the Iwahori-Hecke algebra of the symmetric group whose squares are central. In particular, we describe a commutative subalgebra generated by certain non-central square roots of central elements, and the generic existence of a rank-three submodule of the Hecke algebra contained in the square root of the centre, but not in the centre. The gener...