Related papers: The Segre zeta function of an ideal

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over a field $K$, and let $A$ be a finitely generated standard graded $S$-algebra. We show that if the defining ideal of $A$ has a quadratic initial ideal, then all the graded components of…

We provide a new representation of a refinable shift invariant space with a compactly supported generator, in terms of functions with a special property of homogeneity. In particular these functions include all the homogeneous polynomials…

Let $I\subset S$ be a graded ideal of a standard graded polynomial ring $S$ with coefficients in a field $K$, and let $\text{v}(I)$ be the $\text{v}$-number of $I$. In previous work, we showed that for any graded ideal $I\subset S$…

For each field k, we define an abelian category of rationally decomposed mixed motives with integer coefficients. When k is finite, we show that the category is Tannakian, and we prove formulas relating the behaviour of zeta functions near…

If k is a field of characteristic 0, we prove that the motivic Poincare serie and the motivic Zeta functions associated to a k[[t]]-variety, flat and purely dimensional, are rational.

A computably enumerable equivalence relation (ceer) $X$ is called self-full if whenever $f$ is a reduction of $X$ to $X$ then the range of $f$ intersects all $X$-equivalence classes. It is known that the infinite self-full ceers properly…

We discuss some formulae which express the Alexander polynomial (and thus the zeta-function of the classical monodromy transformation) of a plane curve singularity in terms of the ring of functions on the curve. One of them describes the…

This paper deals with the study of the behaviour of the value semigroup of a curve singularity define over a global field reduced modulo a maximal ideal. We also define a global zeta function of the curve by means of motivic integration…

A cohesive power of a computable structure is an effective ultrapower where a cohesive set acts as an ultrafilter. Let $\omega$, $\zeta$, and $\eta$ denote the respective order-types of the natural numbers, the integers, and the rationals.…

We prove the second author's "denominator conjecture" [40] concerning the common denominators of coefficients of certain linear forms in zeta values. These forms were recently constructed to obtain lower bounds for the dimension of the…

We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by…

We introduce and study subalgebra cotype zeta functions, multivariate zeta functions enumerating fixed-index subalgebras of $R$-algebras of a given cotype. This generalizes and unifies previous works on subalgebra zeta functions and cotype…

We calculate zeta functions for certain orders of rank $3$ defined by standard integral table algebras and integral fusion rings that have irrational-valued irreducible characters. The calculations are obtained from explicit calculations of…

In this paper, we define the edge zeta function of weighted complex. We also present the formula for the edge zeta function of the standard non-uniform complex…

We prove that a certain conjecture holds true and the conjecture states a relationship between the zeta function of a finite category and the Euler characteristic of a finite category.

The special uniformity of zeta functions claims that pure non-abelian zeta functions coincide with group zeta functions associated to the special linear groups. Naturally associated are three aspects, namely, the analytic, arithmetic, and…

We introduce a fundamental homological invariant, called Serre depth, which stratifies Serre's conditions in the same way that depth stratifies the Cohen-Macaulay property. We study the Serre depths of modules over arbitrary Noetherian…

In this paper, motivated by studying special values of zeta functions attached to finite type F_p-schemes, we introduce a category of ``arithmetic C(S^1,R)-modules'' attached to any Dedekind ring R, and compute the 0th K-group of this…

We study zeta functions enumerating subalgebras or ideals of Lie algebras over finite field of prime order $\mathbb{F}_p$. We first develop a general blueprint method for computing zeta functions of $\mathbb{F}_p$-Lie algebras, and…

An orthogonal bundle over a curve has an isotropic Segre invariant determined by the maximal degree of a Lagrangian subbundle. This invariant, and the induced stratifications on moduli spaces of orthogonal bundles, were studied for bundles…