``Radio Sources in Galaxy Clusters at 28.5 GHz''
We present serendipitous detections of radio sources at 28.5 GHz (1 cm), which resulted from our program to image the thermal
Sunyaev-Zeldovich (SZ) effect in 56 galaxy clusters. In a total area of ~0.8 deg^2, we find 64 radio sources with fluxes down to ~0.4 mJy
(greater than 4 sigma) and within 250" from the pointing centers. The spectral indices (S ~ nu^-alpha) of 54 sources with published low-frequency
flux densities lie in the range -0.6 .le. alpha .le. 2, with a mean of 0.77 +/- 0.06 and a median of 0.84. Extending low-frequency surveys of radio
sources toward the galaxy clusters Cl 0016+16, Abell 665, and Abell 2218 to
28.5 GHz and selecting sources with S_1.4 GHz .ge. 7 mJy to form
an unbiased sample, we find a mean spectral index of 0.71 +/- 0.08 and a median of 0.71. We find 4 to 7 times more sources than predicted from
a low-frequency survey in areas without galaxy clusters. This excess cannot be accounted for by gravitational lensing of a background radio
population by cluster potentials, indicating that most of the detected sources are associated with galaxy clusters. The differential source count
slope, gamma ~ 1.96 (dN/dS ~ S^-gamma), is flatter than what is expected for a nonevolving Euclidean population (gamma = 2.5). For the cluster
Abell 2218, the presence of unsubtracted radio sources with S_28.5 GHz .le. 0.5 mJy (~5 sigma) can reduce the observed SZ temperature
decrement by DeltaT ~ 10 to 25 muK. The corresponding overestimation of the Hubble constant derived through a combined analysis of 28.5 GHz
SZ images and X-ray emission observations is less than 6%.