Related papers: Do zeta functions for intermittent maps have branc…

The zeta function of a motive over a finite field is multiplicative with respect to the direct sum of motives. It has beautiful analytic properties, as were predicted by the Weil conjectures. There is also a multiplicative zeta function,…

The Riemann zeta function and the distribution of its nontrivial zeros on the critical line remain central topics in analytic number theory and large-scale computation. This work develops a numerical framework that replaces classical…

The classical inverse problem of recovering a simply connected smooth planar domain from the Steklov spectrum \cite{E} is equivalent to the problem of recovering, up to a conformal equivalence, a positive function $a\in C^\infty({\mathbb…

Let $\sigma$ denote an endomorphism of a smooth algebraic group $G$ over the algebraic closure of a finite field, and assume all iterates of $\sigma$ have finitely many fixed points. Steinberg gave a formula for the number of fixed points…

We study a class $\widehat{\mathfrak{F}}$ of one-dimensional full branch maps introduced in [Doubly Intermittent Full Branch Maps with Critical Points and Singularities; D. Coates, S. Luzzatto, M. Mubarak, 2022], admitting two indifferent…

We consider the resolvent of a second order differential operator with a regular singularity, admitting a family of self-adjoint extensions. We find that the asymptotic expansion for the resolvent in the general case presents unusual powers…

We study the rationality of the Artin-Mazur zeta function of a dynamical system defined by a polynomial self-map of A^1(k), where k is the algebraic closure of the finite field F_p. The zeta functions of the maps f(x)=x^m for (p,m)=1 and…

We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely…

We collect experimental evidence for several propositions, including the following: (1) For each Riemann zero $\rho$ (trivial or nontrivial) and each zeta fixed point $\psi$ there is a nearly logarithmic spiral $s_{\rho, \psi}$ with center…

In this article we introduce a new type of local zeta functions and study some connections with pseudodifferential operators in the framework of non-Archimedean fields. The new local zeta functions are defined by integrating complex powers…

Let $\alpha>1$ be an irrational number of finite type $\tau$. In this paper, we introduce and study a zeta function $Z_\alpha^\sharp(r,q;s)$ that is closely related to the Lipschitz-Lerch zeta function and is naturally associated with the…

In this paper we study the function G(z) := int{0,infinity} y^{z-1}(1 + \exp(y))^{-1} dy, for z in C. We derive a functional equation that relates G(z) and G(1 - z) for all z in C, and we prove: -- That G and the Riemann Zeta function Zeta…

The calculation of the minimum of the effective potential using the zeta function method is extremely advantagous, because the zeta function is regular at $s=0$ and we gain immediately a finite result for the effective potential without the…

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…

We study the entire function zeta(n,s) which is the sum of l to the power -s, where l runs over the positive eigenvalues of the Laplacian of the circular graph C(n) with n vertices. We prove that the roots of zeta(n,s) converge for n to…

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 [19] it was explained how one can naturally associate a Deitmar scheme (which is a scheme defined over the field with one element, $\mathbb{F}_1$) to a so-called "loose graph" (which is a generalization of a graph). Several properties of…

We propose and investigate a strategy toward a proof of the Riemann Hypothesis based on a spectral realization of its non-trivial zeros. Our approach constructs self-adjoint operators obtained as rank-one perturbations of the spectral…

We estimate large and small values of $|\zeta(\rho')|$, where $\rho'$ runs over critical points of the zeta function in the right half of the critical strip, that is, the points where $\zeta'(\rho')=0$ and $1/2<\Re \rho'<1$.

An equivalent, but variant form of the Riemann functional equation is explored, and several discoveries are made. Properties of the Riemann zeta function $\zeta(s)$ from which a necessary and sufficient condition for the existence of zeros…