We know that we do need for high T$_{c}$ : B. Effect of the Frequency Dependence of Fluctuations on T$_{c}$ in s -wave and higher angular momentum pairing (A) is fixed for phonons but not for e-e fluctuations and must be carefully considered so as not to overcount the degrees of freedom and for its effect in renormalizing (B). We will see in Sec. III that (B), (C) and (D) are not independent in the e-ph problem. Arguments will be given that this is true also for the e-e problem. For the case of e-e interactions there is also the additional and important consideration of the distribution of the spectrum of fluctuations, due to the role of inelastic scattering and the difference of normal and anomalous self-energy. We proceed to discuss this immediately. To discuss the role of the spectrum of fluctuations one must turn to the careful analysis of the solutions to the Eliashberg equations. This was done in a beautiful paper for s-wave pairing through phonons by Bergmann and Rainer [21], followed up to examine the role of AFM fluctuations in s-wave pairing [22] and finally for d-wave pairing [23]. Let us start with the simplest situation when the spectrum of fluctuations is extended more or less uniformly over a large range up to a cut-off ω$_{c}$ >> T$_{c}$ . A simple generalization [23, 24] of the McMillan approximate solution [25, 26] to ℓ = 0 pairing gives for λ$_{s}$, λ$_{ℓ}$ of O (1) or smaller. λ$_{ℓ}$ is the dimensionless coupling constant in the ℓ -th particle- particle channel in which pairing is presumed to occur and which therefore occurs in the pairing self-energy in the Eliashberg equation. Since the self-energy must respect the full symmetry of the lattice this always includes the ℓ = 0 channel. For a square lattice in two dimensions or a cubic lattice in three dimensions, the first ℓ = 0 momentum channel included in λ$_{s}$ is the fourth. Since in any reasonable model, the coupling constants go down fast with T$_{c}$ ≈ ω$_{c}$ exp ( − 1 + λ$_{s}$ λ$_{ℓ}$ ) (14) (A) Large spectral weight in the collective fluctuations being exchanged by the fermions, (B) Large coupling of these fluctuations to the fermions, (C) Large frequency scale of the fluctuations and (D) Large density of states of fermions around the chemical potential in a range of frequencies of the upper cut-off of the fluctuations. 20