Undergrad Freqeuncy of Matter Waves Approaches Infinity as Velocity Approaches c

[hisgutsaysmaybe]

TL;DR

If phase velocity = fλ, and as group velocity -> c, λ -> 0 but phase velocity -> c, then does this mean that f -> infinity as group velocity -> c?

I have heard that the phase velocity of matter waves can be represented as c^2/v. But if the wavelength of these matter waves goes to zero as momentum approaches infinity and v approaches c, then does this mean that the frequency of the matter waves approaches infinity, to give the matter wave a finite and nonzero speed?
In a way this might make sense, because E = ymc^2, so hf = ymc^2. However, the time of an event dilates for an observer which is moving with respect to the event, also by a factor of gamma. I had believed that these two phenomena might combine to appear to give the matter wave a constant frequency, regardless of the velocity of the observer.

 

[PeterDonis]

I have heard

Where? Please give a reference.

 

[hisgutsaysmaybe]

From De Broglie's 1924 paper, page 10 (445 of the journal):

Taken from this PDF version: https://www.pwein.at/physics/Lectures/Famous-Papers/Phil-Mag-47-446-1924.pdf

I learned in school that the phase velocity was c^2/v, and I have taken it as fact without trying to understand why yet.