Related papers: Splicing for motivic zeta functions

We define a zeta function woth respect to the twisted Grover matrix of a mixed digraph, and present an exponential expression and a determinant expression of this zeta function. As an application, we give a trace formula with respect to the…

A polynomial counterpart of the Seiberg-Witten invariant associated with a negative definite plumbed 3-manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zeta-function defined by the…

We prove a deletion-contraction formula for motivic Feynman rules given by the classes of the affine graph hypersurface complement in the Grothendieck ring of varieties. We derive explicit recursions and generating series for these motivic…

Let R be a complete discrete valuation ring with maximal ideal generated by pi. Let f(X) in R[X] be a monic polynomial with nonzero discriminant Delta(f). Let s >= v_pi(Delta(f)) + 1. Suppose given a factorisation of f(X) in (R/pi^s R)[X]…

In this paper, we prove that slice polyanalytic functions on quaternions can be considered as solutions of a power of some special global operator with nonconstant coefficients as it happens in the case of slice hyperholomorphic functions.…

This paper studies algebraic and analytic structures associated with the Lerch zeta function, extending the complex variables viewpoint taken in part II. The Lerch transcendent $\Phi(s, z, c)$ is obtained from the Lerch zeta function…

In a previous paper the authors elaborated notions and technique which could be applied to compute such invariants of polynomials as Euler characteristics of fibres and zeta-functions of monodromy transformations associated with a…

In the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the…

In this paper, we give a description of the possible poles of the local zeta function attached to a complex or real analytic mapping in terms of a log-principalization of an ideal associated to the mapping. When the mapping is a…

We provide a formula for the generating series of the zeta function $Z(X,t)$ of symmetric powers $Sym^n X$ of varieties over finite fields. This realizes $Z(X,t)$ as an exponentiable motivic measure whose associated Kapranov motivic zeta…

We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this integral then lead to an adelic interpretation of the so-called…

A meromorphic function on a compact complex analytic manifold defines a $\bc\infty$ locally trivial fibration over the complement of a finite set in the projective line $\bc\bp^1$. We describe zeta-functions of local monodromies of this…

We give a new formula for the special value at s=2 of the Hasse-Weil zeta function for smooth projective fourfolds under some assumptions (the Tate and Beilinson conjecture, finiteness of some cohomology groups, etc.). Our formula may be…

We prove a motivic version of the Poisson formula on the adelic points of a split algebraic torus and apply it to the study of the motivic height zeta function of split projective toric varieties, in the context of the motivic Manin-Peyre…

We introduce the motivic coniveau exact couple of a smooth scheme, in the framework of mixed motives, whose property is to universally give rise to coniveau spectral sequences through realizations. The main result is a computation of its…

We consider the symmetric multiple zeta values in $\mathcal{S}_m$ without modulo $\pi^2$ reduction for indices in which $1$ and $3$ appear alternately. We investigate those values that can be expressed as a polynomial of the Riemann zeta…

Given a projective variety X defined over a finite field, the zeta function of divisors attempts to count all irreducible, codimension one subvarieties of X, each measured by their projective degree. When the dimension of X is greater than…

A generalization of the Apery-like numbers, which is used to describe the special values $\zeta_Q(2)$ and $\zeta_Q(3)$ of the spectral zeta function for the non-commutative harmonic oscillator, are introduced and studied. In fact, we give a…

We define motivic multiple polylogarithms and prove the double shuffle relations for them. We use this to study the motivic fundamental group of the multiplicative group - {N-th roots of unity} and relate it to geometry of modular…

In various contexts, the zeta function of an object splits into a product of $L$-functions. We categorify this product formula for quadratic covers of objects in the following contexts: quadratic extensions of number fields, ramified double…