Let Q be a positive defined n×n matrix and Q[x̲]=x̲TQx̲. The Epstein zeta-function ζ(s;Q), s=σ+it, is defined, for σ>n2, by the series ζ(s;Q)=∑x̲∈Zn\{0̲}(Q[x̲])−s, and is mer...
Suppose that Q is a positive defined n×n matrix, and Q[x̲]=x̲TQx̲ with x̲∈Zn. The Epstein zeta-function ζ(s;Q), s=σ+it, is defined, for σ>n2, by the series ζ(s;Q)=∑x̲∈Zn∖{0&#...
In this paper, we shall establish a hierarchy of functional equations (as a G-function hierarchy) by unifying zeta-functions that satisfy the Hecke functional equation and those corresponding to Maass forms in the framework of the ramified functional...
In the paper, we prove a joint limit theorem in terms of the weak convergence of probability measures on C2 defined by means of the Epstein ζ(s;Q) and Hurwitz ζ(s,α) zeta-functions. The limit measure in the theorem is explicitly given...
We prove a probabilistic limit theorem for the Epstein zeta-function ζ(s;Q) in the interval [N,N+M] as N→∞, using discrete shifts ζ(σ+ikh;Q), where h>0 and σ>n−12 are fixed. Here, Q is a positive-definite...
For j=1,…,r, let Qj be a positive definite nj×nj matrix, and ζ(sj;Qj) denote the corresponding Epstein zeta-function. In this paper, assuming that nj⩾4 is even and x̲TQjx̲∈Z,x̲∈Zr∖{0̲}, a j...
Zeta-functions play a fundamental role in many fields where there is a norm or a means to measure distance. They are usually given in the forms of Dirichlet series (additive), and they sometimes possess the Euler product (multiplicative) when the dom...
In this paper, we study quantum relativistic features of a scalar field around the Rindler–Schwarzschild wormhole. First, we introduce this new class of spacetime, investigating some energy conditions and verifying their violation in a region n...
Integral transforms play a fundamental role in science and engineering. Above all, the Fourier transform is the most vital, which has some specifications—Laplace transform, Mellin transform, etc., with their inverse transforms. In this paper, w...