We present the results of a search for planetary companions orbiting near hot Jupiter planet candidates (Jupiter-size candidates with orbital periods near 3 days) identified in the Kepler data through its sixth quarter of science operations. Special emphasis is given to companions between the 2:1 interior and exterior mean-motion resonances. A photometric transit search excludes companions with sizes ranging from roughly 2/3 to 5 times the size of the Earth, depending upon the noise properties of the target star. A search for dynamically induced deviations from a constant period (transit timing variations or TTVs) also shows no significant signals. In contrast, comparison studies of warm Jupiters (with slightly larger orbits) and hot Neptune-size candidates do exhibit signatures of additional companions with these same tests. These differences between hot Jupiters and other planetary systems denote a distinctly different formation or dynamical history.
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