Related papers: On $p$-adic spectral zeta functions

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…

A derivation of the spectral determinant of the Schr\"odinger operator on a metric graph is presented where the local matching conditions at the vertices are of the general form classified according to the scheme of Kostrykin and Schrader.…

Spectral zeta functions $\zeta(s)$ for the massless scalar fields obeying the Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder are constructed. These functions are defined explicitly in a finite domain of the…

For an arbitrary prime number $p$, we propose an action for bosonic $p$-adic strings in curved target spacetime, and show that the vacuum Einstein equations of the target are a consequence of worldsheet scaling symmetry of the quantum…

We study the spectral zeta functions associated to the radial Schr\"odinger problem with potential V(x)=x^{2M}+alpha x^{M-1}+(lambda^2-1/4)/x^2. Using the quantum Wronskian equation, we provide results such as closed-form evaluations for…

Let $p$ be a prime, and let $\Gamma=\Sp_g(\Z)$ be the Siegel modular group of genus $g$. We study $p$-adic families of zeta functions and Siegel modular forms. $L$-functions of Siegel modular forms are described in terms of motivic…

A review of some recent advances in zeta function techniques is given, in problems of pure mathematical nature but also as applied to the computation of quantum vacuum fluctuations in different field theories, and specially with a view to…

The Shintani cocycle on $\GL_n(\Q)$, as constructed by Hill, gives a cohomological interpretation of special values of zeta functions for totally real fields of degree $n$. We give an explicit criterion for a specialization of the Shintani…

This article is related to construction of zeta strings from $p$-adic ones. In addition to investigation of $p$-adic string for a particular prime number $p$, it is also interesting to study collective effects taking into account all primes…

Using the Weyl quantization we formulate one-dimensional adelic quantum mechanics, which unifies and treats ordinary and $p$-adic quantum mechanics on an equal footing. As an illustration the corresponding harmonic oscillator is considered.…

Geometric zeta functions of Ihara and Hashimoto are generalized to higher rank. The $p$-adic version of the Patterson conjecture is proven.

In this paper we study the spectral asymmetry of (possibly nonselfadjoint) elliptic PsiDO's in terms of the difference of zeta functions coming from different cuttings. Refining previous formulas of Wodzicki in the case of odd class…

This work develops an analytic framework for the study of the $\zeta$-function associated with general sequences of complex numbers. We show that a contour integral representation, commonly used when studying spectral $\zeta$-functions…

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.

We introduce multifractal pressure and dynamical multifractal zeta-functions providing precise information of a very general class of multifractal spectra, including, for example, the fine multifractal spectra of self-conformal measures and…

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…

We introduce multifractal pressure and dynamical multifractal zeta-functions providing precise information of a very general class of multifractal spectra, including, for example, the fine multifractal spectra of graph-directed…

In this paper, we introduce and study two new types of non-abelian zeta functions for curves over finite fields, which are defined by using (moduli spaces of) semi-stable vector bundles and non-stable bundles. A Riemann-Weil type hypothesis…

We give an explicit formula of the coefficients of the Zeta-Function's L-polynomial for algebraic function fields over finite constant fields. Thus, we deduce an expression of the class number of algebraic function fields defined over…

We prove that the zeta-function $\zeta_\Delta$ of the Laplacian $\Delta$ on a self-similar fractals with spectral decimation admits a meromorphic continuation to the whole complex plane. We characterise the poles, compute their residues,…