Related papers: Counting and zeta functions over F1
We show that even $\zeta$-functions may be removed from the $\beta$-functions of general multi-coupling theories up to high loop order by means of coupling redefinitions. For theories whose $\beta$-function is determined by the anomalous…
A simple and elementary derivation of values at integer points for the Riemann's zeta and related functions is reported.
It oftens occurs that Taylor coefficients of (dimensionally regularized) Feynman amplitudes $I$ with rational parameters, expanded at an integral dimension $D= D_0$, are not only periods (Belkale, Brosnan, Bogner, Weinzierl) but actually…
A Master equation has been previously obtained which allows the analytic integration of a fairly large family of functions provided that they possess simple properties. Here, the properties of this Master equation are explored, by extending…
Renormdynamic equations of motion and their solutions are given. New equation for NBD distribution and Riemann zeta function invented. Explicit forms of the z-Scaling functions are constructed.
This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…
We calculate zeta and normal zeta functions of space groups with the point group isomorphic to the cyclic group of order 2. The obtained results are applied to determine the number of subgroups, resp. normal subgroups, of a given index for…
The individual terms of the series representing the Riemann zeta function are examined geometrically from their accumulated plot in the complex plane. Symmetry is identified and determined mathematically for comparison with more traditional…
The connection between Lefschetz formulae and zeta function is explained. As a particular example the theory of the generalized Selberg zeta function is presented. Applications are given to the theory of Anosov flows and prime geodesic…
We initiate the study of spectral zeta functions $\zeta_{X}$ for finite and infinite graphs $X$, instead of the Ihara zeta function, with a perspective towards zeta functions from number theory and connections to hypergeometric functions.…
The purpose of this article is to give an explicit description, in terms of hypergeometric functions over finite fields, of zeta function of a certain type of smooth hypersurfaces that generalizes Dwork family. The point here is that we…
Building on the mapping relations between analytic functions and periodic functions using the abstract operators $\cos(h\partial_x)$ and $\sin(h\partial_x)$, and by defining the Zeta and related functions including the Hurwitz Zeta function…
We introduce the Hadamard topology on the Witt ring of rational functions, giving a simultaneous refinement of the weight and point-counting topologies. Zeta functions of algebraic varieties over finite fields are elements of the rational…
This note contains a short proof of the functional equation for the zeta function.
We define generalised zeta functions associated to indefinite quadratic forms of signature (g-1,1) -- and more generally, to complex symmetric matrices whose imaginary part has signature (g-1,1) -- and we investigate their properties. These…
In this paper, we expand the theory of Weierstrassian elliptic functions by introducing auxiliary zeta functions $\zeta_\lambda$, zeta differences of first kind $\Delta_\lambda$ and second kind $\Delta_{\lambda,\mu}$ where…
The aim of this paper is to show how zeta functions and excision in cyclic cohomology may be combined to obtain index theorems. In the first part, we obtain a local index formula for "abstract elliptic pseudodifferential operators"…
In this article we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle. We start by considering the special case of the star graph with Neumann matching conditions at the center of…
The $\beta\gamma$ system is generalized by complex(rational) powers of the fields, which leads to a corresponding extension on the Fock space. Two different approaches to compute the Green functions of the physical operators are proposed.…
New formulas for approximation of zeta-constants were derived on the basis of a number-theoretic approach constructed for the irrationality proof of certain classical constants. Using these formulas it's possible to approximate certain…