Related papers: Esnault-Levine-Wittenberg indices
In this paper we introduce the additive analogue of the index of a polynomial over finite fields. We study several problems in the theory of polynomials over finite fields in terms of their additive indices, such as value set sizes, bounds…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…
The aim of this Note is to specify the links between the three kinds of Lisbon integrals, trace functions and trace forms with the corresponding D--modules.
This article contains: - Proofs of certain results recently obtained by D. Panyushev. - An addendum to the "inequality of Panyushev". - Calculations of indexes of certain contracted Lie algebras. - Examples of additivity of the index of Lie…
The aim of this paper is to give an explicit formula for the calculation of the Gutzwiller--Maslov index of a Hamiltonian periodic orbit. We identify the index appearing in Gutzwiller's trace formula with a non-trivial extension of the…
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
These lecture notes are intended to give a modest impulse to anyone willing to start or pursue a journey into the theory of Vertex Algebras by reading one of Kac's or Lepowsky-Li's books. Therefore, the primary goal is to provide required…
In this paper we study the notion of isoclinism on Lie-central extensions of Leibniz algebras, this yields to introduce the concept of Lie-isoclinic Leibniz algebras. We provide several equivalent conditions under which Leibniz algebras are…
In a recent preprint, we discussed geometric lifts, and in particular the notion of St\"ackel lift. In this note, we wish to clarify several aspects raised in the comment arXiv:2511.05765.
The aim of this work is to compare the distinct notions of Mal'tsev object in the sense of Weighill and in the sense of Montoli-Rodelo-Van der Linden.
The rapidly increasing number of scientific documents available publicly on the Internet creates the challenge of efficiently organizing and indexing these documents. Due to the time consuming and tedious nature of manual classification and…
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
These notes are based on a sequence of five lectures given to graduate students. The main goal is to prove the so-called Painleve property for semi-simple Frobenius manifolds.
In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.
Back in 1755, Euler explored an interesting array of numbers that now frequently appears in polynomial identities, combinatorial problems, and finite calculus, among other places. These numbers share a strong connection with well-known…
Infinite-dimensional Lie algebras are introduced, which are only partially graded, and are specified by indices lying on cyclotomic rings. They may be thought of as generalizations of the Onsager algebra, but unlike it, or its sl(n)…
These notes deal with metric spaces, Hausdorff measures and dimensions, Lipschitz mappings, and related topics. The reader is assumed to have some familiarity with basic analysis, which is also reviewed.
In this revised version, we add some expository material and references and make some minor corrections.
Talk presented by the second author at the Inaugural Coference of the Asia Pacific Center for Theoretical Physics, Seoul, June 1996. The purpose of this note is to give a resume of the Seiberg-Witten theory in the simplest possible…
An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index transforms of the Lebedev type with products of the modified…