M.S. Thesis Defense in Mathematics: William Wehring 4/9

03/31/2026
By Joris Roos

The Kennedy College of Sciences, Department of Mathematics and Statistics, invites you to attend the Master’s thesis defense by William Wehring on “Estimating L^1 norms of exponential sums”.

Candidate Name: William Wehring
Degree: Master's
Defense Date: Thursday, April 9, 2025
Time: 11 a.m. to noon
Location: Southwick Hall, Room 350W

Thesis Title: Estimating L^1 norms of exponential sums

Committee Members:

• Joris Roos, Ph.D., (Advisor) Department of Mathematics and Statistics, UMass Lowell
• Shiwen Zhang, Ph.D., Department of Mathematics and Statistics, UMass Lowell
• Marco Fraccaroli, Ph.D., Department of Mathematics and Statistics, UMass Lowell

Abstract:
In this thesis, we study the magnitude of $L^1$ norms for various frequency sets. We discuss several examples including the classical Dirichlet kernel, lacunary frequencies and a Cantor set of integers. From there, we study lower bounds for general frequency sets, including the proof of Littlewood's conjecture by McGee, Pigno, and Smith. Non-integer frequency sets are also considered, including an exposition of Ingham's theorem and a result of Hudson and Leckband.