  We make explicit a theorem of Fromm and Goldmakher [arXiv:1706.03002], which
states that one can improve Burgess' bound for short character sums simply by
improving the leading constant in the P\'{o}lya-Vinogradov inequality. Towards
achieving this, we establish explicit versions of several estimates related to
the mean values of real multiplicative functions and the Dickman function.
