What each paper proves, how its results depend on each other, and what exactly has been checked.
The irreducible characters of Sp(2m) at every power of Kostant's element: when they vanish, their value as a signed ratio of root products, and their absolute value as a product of dimensions of GL, Sp and odd SO representations.
A result can carry several marks. Each tile opens its statement; the large ones are the main results.
Zeros of the weighted sums Σn≤m nε(n) of completely multiplicative ε with values ±1: every admissible length is a zero of some ε, infinitely many zeros are rare in measure and generic in category, and for quadratic characters the zeros are explicit.
A result can carry several marks. Each tile opens its statement; the large ones are the main results.
Inside the second inversion stage of the free field of the free group of rank three, two chains of subrings are strict at every step and infinitely many stopping steps of the Dubrovin–Gräter–Hanke series occur; the tool is a sufficient criterion for non-membership.
A result can carry several marks. Each tile opens its statement; the large ones are the main results.