Seminar series
Date
Mon, 17 Jan 2011
Time
16:00 -
17:00
Location
SR1
Speaker
Lillian Pierce
Organisation
Oxford
An old conjecture of Hardy and Littlewood posits that on average, the number of representations of a positive integer N as a sum of k, k-th powers is "very small." Recently, it has been observed that this conjecture is closely related to properties of a discrete fractional integral operator in harmonic analysis. This talk will give a basic introduction to the two key problems, describe the correspondence between them, and show how number theoretic methods, in particular the circle method and mean values of Weyl sums, can be used to say something new in abstract harmonic analysis.