Related papers: Generalizations of the Rowland theorem

In the local, characteristic 0, non archimedean case, we consider distributions on GL(n+1) which are invariant under the adjoint action of GL(n). We prove that such distributions are invariant by transposition. This implies that an…

We prove a generalized version of Renault's theorem for Cartan subalgebras. We show that the original assumptions of second countability and separability are not needed. This weakens the assumption of topological principality of the…

Associated to each random variable $Y$ having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characterizations and specific examples of such generalized numbers…

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

We obtain smoothing estimates for certain nonlinear convolution operators on prime fields, leading to quantitative nonlinear Roth type theorems. Compared with the usual linear setting (i.e. arithmetic progressions), the nonlinear nature of…

We prove a short general theorem which immediately implies some classical results of Hasse, Guillera and Sondow, Paolo Amore, and also Alzer and Richards. At the end we obtain a new representation for the Euler constant gamma. The theorem…

Some mathematical theorems represent ideas that are discovered again and again in different forms. One such theorem is Hall's marriage theorem. This theorem is equivalent to several other theorems in combinatorics and optimization theory,…

We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma…

Normal and composition series of groups enumerated by ordinal numbers are studied. The Jordan-Holder theorem for them is proved.

We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of…

In this paper, we prove a number of results providing either necessary or sufficient conditions guaranteeing that the number of real roots of real polynomials of a given degree is either less or greater than a given number. We also provide…

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

In this article we prove a generalization of the Beurling--Malliavin Majorant Theorem. In more detail, we establish a new sufficient condition for a function to be a Beurling--Malliavin Majorant. Our result is strictly more general than…

In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.

We introduce an generalized action functional describing the equations of motion and the variational equations for any Lagrangian system. Using this novel scheme we are able to generalize Noether's theorem in such a way that to any…

We construct a commutative version of the group ring and show that it allows one to translate questions about the normal generation of groups into questions about the generation of ideals in commutative rings. We demonstrate this with an…

\begin{abstract} We apply the theory of generalized Watson transforms developed in \cite{zheng00} to construct the complementary series of $GL(2,\R)$. \end{abstract}

The theorem presented in this paper allows the creation of large prime numbers (of order up to o(n^2)) given a table of all primes up to n.

We fully classify completely multiplicative sequences which are given by generalised polynomial formulae, and obtain a similar result for (not necessarily completely) multiplicative sequences under the additional restriction that the…

Analogues of invariant theory's well-known Roberts theorem are proved for ternary forms. We established that covariants, contravariants and mixed concomitants of a ternary form are uniquely determined by their lead coefficients.