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In this paper we prove the existence of asymptotic moments, and an estimate on the tails of the limiting distribution, for a specific class of almost periodic functions. Then we introduce the hyperbolic circle problem, proving an estimate on the asymptotic variance of the remainder that improves a result of Chamizo. Applying the results of the first part we prove the existence of limiting distribution and asymptotic moments for three functions that are integrat
The goal of this expository article is a fairly self-contained account of some averaging processes of functions along sequences of the form $(alpha^n x)^{}_{ninmathbb{N}}$, where $alpha$ is a fixed real number with $| alpha | > 1$ and $xinmathbb{R}$
The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction in the sett
The hyperbolic lattice point problem asks to estimate the size of the orbit $Gamma z$ inside a hyperbolic disk of radius $cosh^{-1}(X/2)$ for $Gamma$ a discrete subgroup of $hbox{PSL}_2(R)$. Selberg proved the estimate $O(X^{2/3})$ for the error term
Consider polynomials over ${rm GF}(2)$. We describe efficient algorithms for finding trinomials with large irreducible (and possibly primitive) factors, and give examples of trinomials having a primitive factor of degree $r$ for all Mersenne exponent
In this paper, we use the variational approach to investigate recurrent properties of solutions for stochastic partial differential equations, which is in contrast to the previous semigroup framework. Consider stochastic differential equations with m