Related papers: Recursive formulas for the motivic Milnor basis
We associate with an infinite cyclic cover of a punctured neighborhood of a simple normal crossing divisor on a complex quasi-projective manifold (assuming certain finiteness conditions are satisfied) an element in the Grothendieck ring…
These notes explain how to construct small functorial chain complexes which calculate the derived functors of destabilization (respectively iterated loop functors) in the theory of modules over the mod 2 Steenrod algebra; this shows how to…
The multiple-recursive matrix method for generating pseudorandom vectors was introduced by Niederreiter (Linear Algebra Appl. 192 (1993), 301-328). We propose an algorithm for finding an efficient primitive multiple-recursive matrix method.…
In this note we develop a coalgebraic approach to the study of solutions of linear difference equations over modules and rings. Some known results about linearly recursive sequences over base fields are generalized to linearly (bi)recursive…
We give a recursive formula, expressed in terms of the characteristic tuples, for the Betti numbers of the boundary of the Milnor fiber of an irreducible quasi-ordinary surface. The singular locus of the surface consists of two components,…
We define a method which produces explicit cellular bases for algebras obtained via a Jones basic construction. For the class of algebras in question, our method gives formulas for generic Murphy--type cellular bases indexed by paths on…
The aim of this article is to develop the theory of motivic integration over Deligne-Mumford stacks and to apply it to the birational geometry of stacks.
We construct a theory of motivic integration for smooth rigid varieties. As an application new invariants of degenerations are obtained.
We discuss several approaches to motivic complexes and explicit constructions of the regulator maps from the motivic complexes to Deligne complexes.
By means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial…
We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we…
Multiple modular values are a common generalisation of multiple zeta values and periods of modular forms, and are periods of a hypothetical Tannakian category of mixed modular motives. They are given by regularised iterated integrals on the…
Let $n$ be a maximal nilpotent subalgebra of a complex symmetric Kac-Moody Lie algebra. Lusztig has introduced a basis of U(n) called the semicanonical basis, whose elements can be seen as certain constructible functions on varieties of…
Brown showed that the affine ring of the motivic path torsor $\pi_1^{\text{mot}}(\mathbb{P}^1 \backslash \left\{0,1,\infty\right\}, \vec{1}_0, -\vec{1}_1)$, whose periods are multiple zeta values, generates the Tannakian category…
We present an algorithm to compute values L(s) and derivatives of L-functions of motivic origin numerically to required accuracy. Specifically, the method applies to any L-series whose Gamma-factor is a product of any number of…
We study a new type of sequences whose elements are defined in terms of the position, sign and magnitude of another element of the sequence. The name ultra-recursive comes from the fact that these sequences possess terms that are generated…
A minimal system of homogeneous generating elements of the algebra of covariants for the binary form of degree 8 is calculated.
Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (>= -1) of all the interparticle distances r_ij, multiplied by an exponential containing an arbitrary…
In this short note we use the notion of power structure over the Grothendieck ring of complex algebraic varieties to study generating series of classes of Hilbert schemes of points on complex orbifolds.
We study the motivic Grothendieck group of algebraic varieties from the point of view of stable birational geometry. In particular, we obtain a counter-example to a conjecture of M. Kapranov on the rationality of motivic zeta-function.