Related papers: Quantization coefficients for uniform distribution…
For $-\pi\leq\beta_1<\beta_2\leq\pi$ denote by $\Phi_{\beta_1,\beta_2}(Q)$ the number of algebraic numbers on the unit circle with arguments in $[\beta_1,\beta_2]$ of degree $2m$ and with elliptic height at most $Q$. We show that \[…
The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of trigonometric polynomials with frequencies from an arbitrary finite set…
We compute the depth and (give bounds for) the regularity of generalized binomial edge ideals associated with generalized block graphs.
We consider the following construction of quantization. For a Riemannian manifold $M$ the space of forms on $T^*M$ is made into a space of (full) symbols of operators acting on forms on $M$. This gives rise to the composition of symbols,…
We compute the uniform probability that finitely many polynomials over a finite field are pairwise coprime and compare the result with the formula one gets using the natural density as probability measure. It will turn out that the formulas…
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…
The representation of a given quantity with less information is often referred to as `quantization' and it is an important subject in information theory. In this paper, we have considered absolutely continuous probability measures on unit…
While studying a characteristic number of manifolds we noticed that the calculation was simply computing a multiple of a multinomial coefficient. We were, at the time, interested in computing the greatest common divisor of these…
We consider polynomials on the unit circle defined by the recurrence relation \Phi_{k+1}(z) = z \Phi_{k} (z) - \bar{\alpha}_{k} \Phi_k^{*}(z) for k \geq 0 and \Phi_0=1. For each n we take \alpha_0, \alpha_1, ...,\alpha_{n-2} i.i.d. random…
An optimal bound on the quantiles of a certain kind of distributions is given. Such a bound is used in applications to Berry--Esseen-type bounds for nonlinear statistics.
Consider the integer points lying on the sphere of fixed radius projected onto the unit sphere. Duke showed that, on congruence conditions for the radius squared, these points equidistribute. To further this study of equidistribution, we…
We give a unified statement and proof of a class of wellknown mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on…
We derive a formula for the level spacing probability distribution in quantum graphs. We apply it to simple examples and we discuss its relation with previous work and its possible application in more general cases. Moreover, we derive an…
In the present paper, we define Morse-Bott functions on manifolds with boundary which are generalizations of Morse functions and show Morse-Bott inequalities for these manifolds.
Exact expressions for three-dimensional potential and force yield due to uniform singularity distributed on a finite at rectangular surface have been presented. The expressions, valid throughout the physical domain, have been found to be…
We prove a Fourier restriction result, uniform over a certain collection of reference measures, for some indices in the Stein-Tomas range.
In 1969, Delange has proved a general criterion for uniform distribution of additive functions. In this paper, we study the uniform distribution of a special class of polynomially-defined additive functions where the moduli is allowed to…
We explore a definition of uniformity on noncompact manifolds that does not require a Riemannian metric, but is equivalent to bounded gemetry. These are unfinished research notes (and will likely never be published), but since they were…
Nonextensive quantum gas distributions are investigated on the basis of the factorization hypothesis of compound probability required by thermodynamic equilibrium. It is shown that the formalisms of Tsallis nonextensive statistical…