Related papers: Variations on theorems of Mertens
We develop convergent variational perturbation theory for quantum statistical density matrices. The theory is applicable to polynomial as well as nonpolynomial interactions. Illustrating the power of the theory, we calculate the…
We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…
We revisit the questions of density of smooth functions, and differential forms, in Sobolev spaces on Riemannian manifolds. We carefully show equivalence of weak covariant derivatives to weak partial derivatives.
We discuss various effective forms of Chebotarev's density theorem, answering a question of Serre and a question of Murty, Murty and Seradha.
We study \L o\'s's theorem in a choiceless context. We introduce some variants of \L o\'s's theorem. These variants seem weaker than \L o\'s's theorem, but we prove that these are equivalent to \L o\'s's theorem.
We study the distribution of integral points on log varieties.
The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…
We present and prove the version of Marstrand's theorem for discrete metric space. We provide explicit estimates of the quotient of upper and lower densities of measures on this space.
We shall present an elementary approach to extremal decompositions of (quantum) covariance matrices determined by densities. We give a new proof on former results and provide a sharp estimate of the ranks of the densities that appear in the…
A relationship between the Riemann zeta function and a density on integer sets is explored. Several properties of the examined density are derived.
We prove a function-field version of Chebotarev's density theorem in the framework of difference algebraic geometry by developing the notion of Galois coverings of generalised difference schemes, and using Hrushovski's twisted Lang-Weil…
The paper deals with a generalisation of uniform distribution. The analogues of Weyl's criterion are derived.
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
This text is devoted to the theory of varieties, which provides an important tool, based in universal algebra, for the classification of regular languages. In the introductory section, we present a number of examples that illustrate and…
With the help of Van der Corput lemmas, decay estimates are proven for Fourier transforms of mixed homogeneous hypersurface measures with densities that can be quite irregular. The primary results are local in nature, but can be extended to…
We consider deconvolution from repeated observations with unknown error distribution. So far, this model has mostly been studied under the additional assumption that the errors are symmetric. We construct an estimator for the non-symmetric…
Linear wavelet density estimators are wavelet projections of the empirical measure based on independent, identically distributed observations. We study here the law of the iterated logarithm (LIL) and a Berry-Esseen type theorem. These…
The notion of density of a finite set is discussed. We proof a general theorem of set theory which refines Bose-Einstein distribution.
We show that a conceptually simple covering technique has surprisingly rich applications to density theorems and conjectures on patterns in sets involving set differences. These applications fall into three categories: (i) analogues of…
We completely characterize the weak differentiability (or, in other words Gateaux differentiability) of the norm in the spaces of bounded multilinear maps. Also, we obtain a multilinear generalization of the well-known Bhatia-\v{S}emrl…