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Analytic Number Theory Graduate Student Seminar April 11, 2017 (04:00 PM PDT - 05:00 PM PDT)
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Location: MSRI: Baker Board Room
Speaker(s) Robert Fraser (University of British Columbia), Alexander Walker (Brown University)
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4.00pm:​ Rob Fraser

​Title: ​​Explicit ​s​alem ​s​ets in p-​a​dic ​f​ields

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.

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