We present serendipitous detections of radio sources at 28.5 GHz (1 cm
), which resulted from our program to image the thermal Sunyaev-Zeldov
ich (SZ) effect in 56 galaxy clusters. In a total area of similar to 0
.8 deg(2), we find 64 radio sources with fluxes down to similar to 0.4
mJy (greater than 4 sigma) and within 250 '' from the pointing center
s. The spectral indices (S proportional to nu(-alpha)) of 54 sources w
ith published low-frequency flux densities lie in the range -0.6 less
than or similar to alpha less than or similar to 2, with a mean of 0.7
7 +/- 0.06 and a median of 0.84. Extending low-frequency surveys of ra
dio sources toward the galaxy clusters Cl 0016 + 16, Abell 665, and Ab
ell 2218 to 28.5 GHz and selecting sources with S-1.4 GHz greater than
or equal to 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 mor
e 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, indica
ting that most of the detected sources are associated with galaxy clus
ters. The differential source count slope, gamma similar to 1.96 (dN/d
S proportional to S-gamma), is flatter than what is expected for a non
evolving Euclidean population (gamma = 2.5). For the cluster Abell 221
8, the presence of unsubtracted radio sources with S-28.5 GHz less tha
n or equal to 0.5 mJy (similar to 5 sigma) can reduce the observed SZ
temperature decrement by Delta T similar to 10 to 25 mu K. The corresp
onding overestimation of the Hubble constant derived through a combine
d analysis of 28.5 GHz SZ images and X-ray emission observations is le
ss than 6%.