There are periodically false proofs of the rapid decay (RD) Property (see this introduction by Chatterji and Saloff-Coste) for cocompact lattices in semisimple Lie groups (Valette's conjecture). This is a functional-analytic property of these groups. As far as I understand, the wrong proof typically makes use of some quantitative decreasing of coefficients, and this involves a "constant". The issue (sorry if I'm a bit imprecise) being that this "constant" actually depends on the dimension of something related to the induced representation restricted to a maximal compact subgroup.

There are periodically false proofs of the rapid decay (RD) Property (see Chatterji and Saloff-Coste - Introduction to the property of rapid decay) for cocompact lattices in semisimple Lie groups (Valette's conjecture). This is a functional-analytic property of these groups. As far as I understand, wrong proofs typically make use of some quantitative decreasing of coefficients, and this involves a "constant". The issue (sorry if I'm a bit imprecise) being that this "constant" actually depends on the dimension of something related to the induced representation restricted to a maximal compact subgroup.