Mengdi Wang: Local Fourier uniformity of divisor functions

Abstract:

 Let \(d_k(n)\) represent the \(k\)-fold divisor function, counting the ways \(n\) can be expressed as the product of \(k\) natural numbers. In this presentation, we will introduce the local uniformity of \(k\)-fold divisor functions first. Then we plan to investigate the current research on the local correlation between \(k\)-fold divisor functions and linear phase functions in very short intervals.