Arithmetic sensitivity of cumulant growth in lacunary sums: transcendental versus algebraic ratio limits

Christoph Aistleitner, Zakhar Kabluchko, Joscha Prochno

We study the asymptotic behavior of cumulants of lacunary trigonometric sums $S_n(\omega ):={\sum }_{k=1}^n\cos (2\pi a_k\omega )$, $\omega \in [0,1]$, and show that cumulant growth is highly sensitiv…