Related papers: On distribution formulas for complex and $\ell$-ad…

We study asymptotic distribution of zeros of random holomorphic sections of high powers of positive line bundles defined over projective homogenous manifolds. We work with a wide class of distributions that includes real and complex…

For any finite group G and integer i, let $\mathcal{H}^i(G)$ be the set of all the isomorphism classes of the Galois cohomology groups $\hat{H}^i(K/k,E_K)$, where K/k runs over all the unramified G-extension of number fields and E_K denotes…

The aim of this paper is to present an algorithm the complexity of which is polynomial to compute the semi-simplified modulo $p$ of a semi-stable $\Q_p$-representation of the absolute Galois group of a $p$-adic field (\emph{i.e.} a finite…

The Coleman-Ihara formula expresses Soule's $p$-adic characters restricted to $p$-local Galois group as the Coates-Wiles homomorphism multiplied by $p$-adic $L$-values at positive integers. In this paper, we show an analogous formula that…

In the frame of Mahler's method for algebraic independence we show that the algebraic relations over Q linking the values of functions solutions of a system of functional equations come from the algebraic relations between the functions…

We propose an integral geometric approach for computing dual distributions for the parameter distributions of multilinear models. The dual distributions can be computed from, for example, the parameter distributions of conics, multiple view…

Let $K$ be a finitely generated extension of $\mathbb{Q}$. We consider the family of $\ell$-adic representations ($\ell$ varies through the set of all prime numbers) of the absolute Galois group of $K$, attached to $\ell$-adic cohomology of…

We classify all cubic function fields over any finite field, particularly developing a complete Galois theory which includes those cases when the constant field is missing certain roots of unity. In doing so, we find criteria which allow…

We discuss the computational complexity of solving linear programming problems by means of an analog computer. The latter is modeled by a dynamical system which converges to the optimal vertex solution. We analyze various probability…

Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…

We point out the relevance of the Differential Galois Theory of linear differential equations for the exact semiclassical computations in path integrals in quantum mechanics. The main tool will be a necessary condition for complete…

We introduce a new collection of partially global Galois cohomology classes subsuming both plectic Heegner points and mock plectic invariants. The former are recovered as localizations of plectic Heegner classes, while the latter arise as…

Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation…

Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…

Charged multiplicity distribution in a pseudo-rapidity window is formulated under the assumption that the charge conservation is satisfied in the full phase space. At first, we analyze measured charged particle multiplicity distributions in…

This is a gentle introduction to Colombeau nonlinear generalized functions, a generalization of the concept of distributions such that distributions can freely be multiplied. It is intended to physicists and applied mathematicians who…

For a finite group $G$, we introduce a generalization of norm relations in the group algebra $\mathbb Q[G]$. We give necessary and sufficient criteria for the existence of such relations and apply them to obtain relations between the…

We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices. Each finite directed acyclic graph admits countably many structures of a generalized…

We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by…

For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…