CARMA SEMINAR Speaker: Kevin Hare, University of Waterloo Title: Stolarsky's Conjecture and the sum of digits function Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle Time and Date: 4:00 pm, Thu, 7th Feb 2013 Abstract: Let $s_q(n)$ be the sum of the $q$-ary digits of $n$. For example $s_{10}(1729) = 1 + 7 + 2 + 9 = 19$. It is known what $s_q(n)$ looks like "on average". It can be shown that $s_q(n^h)$ looks $h$ times bigger "on average". This raises the question: is the ratio of these two things $h$ on average? In this talk we will give some history on the sum of digits function, and will give a proof of one of Stolarsky's conjecture concerning the minimal values of the ratio of $s_q(n)$ and $s_q(n^h)$. [Permanent link]