Character levels and character bounds for finite classical groups

Abstract

The main results of the paper develop a level theory and establish strong character bounds for finite classical groups, in the case that the centralizer of the element has small order compared to |G|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$|G|$\\end{document} in a logarithmic sense.