|Location:||MSRI: Baker Board Room|
4.00pm: Rob Fraser
Title: Explicit salem sets in p-adic fields
Abstract: We obtain a pointwise Fourier decay estimate for a measure supported on the well-approximable numbers in ZZ_p. We compare the proof of this estimate to the proof of a similar estimate obtained by Kaufman for the well-approximable numbers in [0,1].
4.30pm: Alex Walker
Title: Long Arithmetic Progressions with Restricted Digits
Abstract: What is the length of the longest arithmetic progression that omits a base-b digit? In this talk, I'll provide an exact expression for this maximal length, as a function of the base. The solution introduces an arithmetic function which is of independent interest: \rho(n), the largest integer less than n whose radical divides n. Techniques in linear programming show that \rho(n) \sim n in average value, and more precise versions of this statement are the subject of ongoing joint work with Aled Walker.