7 problems

Main conjecture.

General weighted sine-sum oscillation conjecture.

Quarter-period sine-sine oscillation conjecture.

Let … with the parameters and primed summation convention used in the paper. Cosine-sine oscillation conjecture. … This predicts unbounded oscillation at scale $x^{1/4}$. The motiv…

Sun's conjecture. There exist positive integers $T_1,T_2,\ldots$ such that

Gaussian fluctuation conjecture. One has

Let $u(x,t)$ denote the shape of a vibrating string, where $x$ is the spatial variable and $t$ is time. A trigonometric series is a series formed from trigonometric functions such…