Let A be an algebra, and let θ, φ be ring automorphisms of A. An additive mapping H : A → A is called a θ, φ -derivation if H xy H x θ y φ x H y for all x, y ∈ A. Moreover, an additive mapping F : A → A is said to be a generalized θ, φ -derivation if there exists a θ, φ derivation H : A → A such that F xy F x θ y φ x H y for all x, y ∈ A. In this paper, we investigate the superstability of gene...

Let k be a number field and O the ring of integers. In the previous paper [T06] we study the Dirichlet series counting discriminants of cubic algebras of O and derive some density theorems on distributions of the discriminants by using the theory of zeta functions of prehomogeneous vector spaces. In this paper we consider these objects under imposing finite number of splitting conditions at non...

If K is a complete non-archimedean field with a discrete valuation and f ∈ K[X ] is a polynomial with non-vanishing discriminant. The first main result of this paper is about connecting the number of roots of f to the number of roots of its reduction modulo a power of the maximal ideal of the valuation ring of K. If the polynomial f is regular, we give an algorithmic method to compute the exact...

For the whole paper, K denotes an algebraically closed field endowed with a nontrivial non-archimedean complete absolute value | |. The corresponding valuation is v := − log | | with value group Γ := v(K). The valuation ring is denoted by K. Note that the residue field K̃ is algebraically closed. In Theorem 1.3, §8 and in the second part of §9, we start with a field K endowed with a discrete val...

Let F be a local non-Archimedean field with ring of integers o and uniformizer ̟. Let X be a one-dimensional formal o-module of F -height n over the algebraic closure F of the residue field of o. By the work of Drinfeld, the universal deformation X of X is a formal group over a power series ring R0 in n − 1 variables over the completion of the maximal unramified extension ônr of o. For h ∈ {0, ....

We study low order terms of Emerton’s spectral sequence for simply connected, simple groups. As a result, for real rank 1 groups, we show that Emerton’s method for constructing eigenvarieties is successful in cohomological dimension 1. For real rank 2 groups, we show that a slight modification of Emerton’s method allows one to construct eigenvarieties in cohomological dimension 2. Throughout th...

The local theory of complex dimensions for real and $$p$$ -adic fractal strings describes oscillations that are intrinsic to the geometry, dynamics spectrum archimedean nonarchimedean strings. We aim develop a global adèlic in order reveal oscillatory nature understand Riemann hypothesis terms vibrations resonances present simple natural construction self-similar any rational (i.e., Minkowski) ...

Assuming absolute continuity of marginals, we give the distribution for sums of dependent random variables from some class of Archimedean copulas and the marginal distribution functions of all order statistics.We use conditional independence structure of random variables from this class of Archimedean copulas and Laplace transform. Additionally, we present an application of our results to VaR e...

The aim of this paper is that of discussing closed graph theorems for bornological vector spaces in a self-contained way, hoping to make the subject more accessible to non-experts. We will see how to easily adapt classical arguments of functional analysis over R and C to deduce closed graph theorems for bornological vector spaces over any complete, non-trivially valued field, hence encompassing...

Axiomatizations of measurement systems usually require an axiom--called an Archimedean axiom-that allows quantities to be compared. This type of axiom has a different form from the other measurement axioms, and cannot-except in the most trivial cases-be empirically verified. In this paper, representation theorems for extensive measurement structures without Archimedean axioms are given. Such st...