A conjecture for arithmetic spherical maximal functions
arXiv:2605.22712
Abstract
For 24 years, it has been an open problem to obtain improved bounds, for the maximal function over a sparse sequence of discrete spherical averages, going beyond the range for the full discrete spherical maximal function. I formulate a conjecture to characterize the boundedness of such maximal functions and state a theorem in support of it.
Apologies for not sharing this on the arXiv sooner