His dissertation, which was supervised by Tamarkin, was An Extended Theory of Lucas' Functions. Lehmer's life over the next few years involved moving from place to place hoping for a permanent university post in the particularly difficult times of the Great Depression.
Kanyang disertasyon, na kung saan ay supervised by Tamarkin, ay isang Extended teorya ng Lucas' function. Lehmer ng buhay sa susunod na ilang taon na kasangkot lumipat mula sa lugar sa lugar hoping para sa isang permanenteng unibersidad post sa mahirap lalo na beses ng Great Depression.