This is the first part of two presentations on Littlewood's problem for nonharmonic Fourier series, which provides a lower bound on the 1-norm of trigonometric polynomials.
Reference:
P. Jaming, C. Saba. From Ingham to Nazarov’s inequality: a survey on some trigonometric inequalities. Adv. Pure Appl. Math. 15, No. 3, 12-76 (2024).