Sparse Bounds for Discrete Spherical Maximal Averages

Series: 
Analysis Seminar
Wednesday, September 20, 2017 - 13:55
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Georgia Tech
Organizer: 
 Magyar, Stein, and Wainger proved a discrete variant in Zd of the continuous spherical maximal theorem in Rd for all d ≥ 5. Their argument proceeded via the celebrated “circle method” of Hardy, Littlewood, and Ramanujan and relied on estimates for continuous spherical maximal averages via a general transference principle. In this talk, we introduce a range of sparse bounds for discrete spherical maximal averages and discuss some ideas needed to obtain satisfactory control on the major and minor arcs. No sparse bounds were previously known in this setting.