Department of

February 2017 March 2017 April 2017 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 1 2 3 4 1 5 6 7 8 9 10 11 5 6 7 8 9 10 11 2 3 4 5 6 7 8 12 13 14 15 16 17 18 12 13 14 15 16 17 18 9 10 11 12 13 14 15 19 20 21 22 23 24 25 19 20 21 22 23 24 25 16 17 18 19 20 21 22 26 27 28 26 27 28 29 30 31 23 24 25 26 27 28 29 30

Thursday, March 2, 2017

**Abstract:** In this talk we will discuss some old and new conjectures about the behavior of sums of arithmetic functions in short intervals, along with analogues of these conjectures in a function field setting that have been proved in recent years. We will pay particular attention to some surprising phenomena that comes into play, and a decomposition of arithmetic functions in a function field setting that helps elucidate what's happening.