On the p-irrationality of character values


I will discuss the irrationality at a prime $p$ of the values of irreducible characters of a finite group. Among $p$’-degree characters, this irrationality behaves very nicely due to its conection with Navarro’s refinement of the celebrated McKay conjecture. I will present some recent work on the continuity of $p$-irrationality of $p$’-degree characters, bounding almost $p$-rational characters, and bounding odd-degree characters. Some results are joint with G. Malle and A. Maroti.