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We study the variance of the random variable that counts the number of lattice points in some shells generated by a special class of finite type domains in $mathbb R^d$. The proof relies on estimates of the Fourier transform of indicator functions of convex domains.
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
In this short note, we reformulate the task of calculating the pair correlation statistics of a Kronecker sequence as a lattice point counting problem. This can be done analogously to the lattice based approach which was used to (re-)prove the famous
We give two variations on a result of Wilkies on unary functions defianble in $mathbb{R}_{an,exp}$ that take integer values at positive integers. Provided that the functions grows slower than the function $2^x$, Wilkie showed that is must be eventual
In this paper, we derive some identities involving special numbers and moments of random variables by using the generating functions of the moments of certain random variables. Here the related special numbers are Stirling numbers of the first and se
This survey paper examines the effective model theory obtained with the BSS model of real number computation. It treats the following topics: computable ordinals, satisfaction of computable infinitary formulas, forcing as a construction technique, ef