Related papers: Graph Zeta Function and Gauge Theories
A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structure, plus countably many special…
We study free scalar field theory on a graph, which gives rise to a modified version of discrete Green's function on a graph studied in \cite{CY}. We show that this gives rise to a graph invariant, which is closely related to the 2-dim…
We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…
Extending the Eulerian functions, we study their relationship with zeta function of several variables. In particular, starting with Weierstrass factorization theorem (and Newton-Girard identity) for the complex Gamma function, we are…
We show that if a graph $G$ has average degree $\bar d \geq 4$, then the Ihara zeta function of $G$ is edge-reconstructible. We prove some general spectral properties of the edge adjacency operator $T$: it is symmetric for an indefinite…
In this note, we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larger class of manifolds known as convex co-compact manifolds…
We give several unequivalent notions of convergency of meromorphic functions and more generally meromorphic mappings (strong, weak, $\Gamma $-convergency and some others). Relations between them are investigated. A version of Rouche theorem…
We find necessary and sufficient conditions for gauge invariance of the action of Double Field Theory (DFT) as well as closure of the algebra of gauge symmetries. The so-called weak and strong constraints are sufficient to satisfy them, but…
The present essay aims at investigating whether and how far an algebraic analysis of the Zeta Function and of the Riemann Hypothesis can be carried out. Of course the well-established properties of the Zeta Function, explored in depth in…
We provide several properties of the geometric polynomials discussed in earlier works of the authors. Further, the geometric polynomials are used to obtain a closed form evaluation of certain series involving Riemann's zeta function.
We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at odd positive integers.
In this paper, we study the relation between the zeta function of a Calabi-Yau hypersurface and the zeta function of its mirror. Two types of arithmetic relations are discovered. This motivates us to formulate two general arithmetic mirror…
We show that if the Riemann Hypothesis is true, then in a region containing most of the right-half of the critical strip, the Riemann zeta-function is well approximated by short truncations of its Euler product. Conversely, if the…
In recent work by the authors, a connection between Feynman's path integral and Fourier integral operator $\zeta$-functions has been established as a means of regularizing the vacuum expectation values in quantum field theories. However,…
Recently the duality map between electric-like asymptotic charges of $p$-form gauge theories is studied. The outcome is an existence and uniqueness theorem and the topological nature of the duality map. The goal of this work is to extend…
The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…
The paper describes a method for calculating values of Riemann's Zeta function within the critical strip 0< {\sigma} <1 and on its boundary. The approach is based on the "Alternating Zeta function" {\eta}(s). The actual Riemann Zeta…
In this paper we provide a proof of the Riemann Hypothesis by relating the non-trivial zeros of the zeta function to a certain Sturm-Liouville eigenvalue problem on a finite interval.
We construct variants of the Riemann zeta function with convenient properties and make conjectures about their dynamics; some of the conjectures are based on an analogy with the dynamical system of zeta. More specifically, we study the…
We investigate certain arithmetic properties of field theories. In particular, we study the vacuum structure of supersymmetric gauge theories as algebraic varieties over number fields of finite characteristic. Parallel to the Plethystic…