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

Explicit Improvements to the Burgess Bound Via P\'olya-Vinogradov