相关论文: Motivic integrals and functional equations

We find an arc-parameterization of the contour on which an given analytic function has constant modulus. This contour is seen to satisfy a differential equation which we explicitly give.

Given a pure motive $M$ over $\mathbb{Q}$ with a multilinear algebraic structure $\mathsf{s}$ on $M$, and given a representation $V$ of the group respecting $\mathsf{s}$, we describe a functorial transfer $M^V$. We formulate a criterion…

The goal of this paper is to count the number of distinct functions of n variables, up to permutation of the variables, that can be constructed using each variable exactly once, without constants, using only the operations of addition,…

We determine the relation between the local Euler obstruction $Eu_f$ of a holomorphic function $f$ and different generalizations of the Milnor number for functions on singular spaces.

In this paper we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which…

Motivic local systems over a curve in finite characteristic form a countable set endowed with an action of the absolute Galois group of rational numbers commuting with the Frobenius map. I will discuss three series of conjectures about such…

Inspired by the work of Deninger, we present a formula that relates the Mahler measure of a two-variable variant of cyclotomic polynomial to regulator of class in motivic cohomology associated to cyclotomic fields and linear combination of…

In [arXiv:2212.04969], the authors stated some conjectures on the variance of certain sums of the divisor function $d_k(n)$ over number fields, which were inspired by analogous results over function fields proven in [arXiv:2107.01437].…

Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…

In this paper I give an evaluation of a functional integral by means of a series in functional derivatives, first of all we propose a differential equation of first order and solve it by iterative methods, to obtain a series for the…

A rational function is the ratio of two complex polynomials in one variable without common roots. Its degree is the maximum of the degrees of the numerator and the denominator. Rational functions belong to the same class if one turns into…

A recursive method is given for finding generating functions which enumerate rooted hypermaps by number of vertices, edges and faces for any given number of darts. It makes use of matrix-integral expressions arising from the study of…

We investigate forms of the Hopf invariant one problem in motivic homotopy theory over arbitrary base fields of characteristic not equal to $2$. Maps of Hopf invariant one classically arise from unital products on spheres, and one…

Given a model in algebraic statistics and some data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying…

A multivariate interpolation formula (MVIF) over finite fields is presented by using the proposed Kronecker delta function. The MVIF can be applied to yield polynomial relations over the base field among homogeneous symmetric rational…

Influence diagrams represent decision-making problems with interdependencies between random events, decisions, and consequences. Traditionally, they have been solved using algorithms that determine the expected utility-maximizing decision…

This paper presents analytical solvers for four common types of algebraic equations encountered in robot kinematics: single trigonometric equations, single-angle trigonometric systems, two-angle trigonometric systems, and bilinear two-angle…

In this work at first the relation the Mittag-Lefler function to the exponential is given. The results are applied to the construction of the solution of Cauchy problem for ordinary linear operator differential equations with constant…

We give a necessary condition for a meromorphic function in several variables to give rise to a Milnor fibration of the local link (respectively of the link at infinity). In the case of two variables we give some necessary and sufficient…

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…