Related papers: A Note on Absolute Derivations and Zeta Functions

We take another look at the so-called quasi-derivation relations in the theory of multiple zeta values, by giving a certain formula for the quasi-derivation operator. In doing so, we are not only able to prove the quasi-derivation relations…

We investigate the location of zeros and poles of a dynamical zeta function arizing in a class of lattice spin models introduced in the 60-ties by M. Kac. The transfer operator method allows us to prove the xistence of infinitely nontrivial…

Some aspects of the multiplicative anomaly of zeta determinants are investigated. A rather simple approach is adopted and, in particular, the question of zeta function factorization, together with its possible relation with the…

Let $Z(t)$ be the classical Hardy function in the theory of the Riemann zeta-function. The main result in this paper is that if the Riemann hypothesis is true then for any positive integer $n$ there exists a $t_{n}>0$ such that for…

In this note we prove the Davies-Foda-Jimbo-Miwa-Nakayashiki conjecture on the asymptotics of the composition of n quantum vertex operators for the quantum affine algebra U_q(\hat sl_2), as n goes to infinity. For this purpose we define and…

While the definition of a fractional integral may be codified by Riemann and Liouville, an agreed-upon fractional derivative has eluded discovery for many years. This is likely a result of integral definitions including numerous constants…

We prove Witten zeta function of a root system $\Phi$ has high-order vanishing at negative even integers, using an integral representation involving the Hurwitz zeta function. This settles a conjecture of Kurokawa and Ochiai for a large…

We construct Sugawara operators for the quantum affine algebra of type $A$ in an explicit form. The operators are associated with primitive idempotents of the Hecke algebra and parameterized by Young diagrams. This generalizes a previous…

In this paper we discuss various potentials related to the Riemann zeta function and the Riemann Xi function. These potentials are modified versions of Morse potentials and can also be related to modified forms of the radial harmonic…

We introduce a new method to detect the zeros of the Riemann zeta function which is sensitive to the vertical distribution of the zeros. This allows us to prove there are few `half-isolated' zeros. By combining this with classical methods,…

We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling constants or temperatures. We are led to…

A Hadamard factorization of the Riemann Xi-function is constructed to characterize the zeros of the zeta function.

We discuss a possible spectral realization of the Riemann zeros based on the Hamiltonian $H = xp$ perturbed by a term that depends on two potentials, which are related to the Berry-Keating semiclassical constraints. We find perturbatively…

We explore the meromorphic structure of the $\zeta$-function associated to the boundary eigenvalue problem of a modified Sturm-Liouville operator subject to spectral dependent boundary conditions at one end of a segment of length $l$. We…

We extend the formulation of pseudo-Hermitian quantum mechanics to eta-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta. In particular, we give the details of the construction of the physical Hilbert space,…

It is shown that the estimates obtained by Manfredo P. do Carmo and Detang Zhou, in their paper "Eigenvalue estimate on complete noncompact Riemannian manifolds and applications", for the first eigenvalue of the Laplace-Beltrami operator on…

For relativistic closed systems, an operator is explained which has as stationary eigenvalues the squares of the total cms energies, while the wave function has only half as many components as the corresponding Dirac wave function. The…

In this article, we study the zeta function $\zeta_q$ associated to the Laplace operator $\Delta_q$ acting on the space of the smooth $(0,q)$-forms with $q=0,\ldots,n$ on the complex projective space $\mathbb{P}^n(\mathbb{C})$ endowed with…

Simple and analytically tractable expressions for functional determinants are known to exist for many cases of interest. We extend the range of situations for which these hold to cover systems of self-adjoint operators of the…

In [16] G. Shimura introduced a family of invariant differential operators that play a key role in the study of nearly holomorphic automorphic forms, and he asked for a determination of their \textquotedblleft domain of…