On the Dirichlet divisor problem in short intervals

We present several new results involving Δ(x+U)−Δ(x), where U=o(x) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta(x):=\sum_{n\leq x}d(n)-x\log x-(2\gamma-1)x $$\end{document} is the error term in the classical Dirichlet divisor problem.