Military Slave Rentals, the Construction of Army Fortifications, and the Navy Yard in Pensacola, Florida, 1824-1863

In the first half of the nineteenth century, expansion of the abolitionist movement led to increasing pressure on the federal government to substantiate military labor policies in regard to the construction of defense installations and public works projects. The manifestation of this pressure resulted in the passage of a law in 1842 by Congress that required government agencies to account for the use of slave labor. As a result, a resolution of the House of Representatives lStin stant forced Navy Secretary A. P. Upshur to respond to questioning on August 10, 1842. When asked what number of colored persons there were in the Navy, he replied, There are no slaves in the navy, except only in a few cases, in which officers have been permitted to take their personal servants, instead of employing them from the crews. He continued by reminding the committee there is a regulation of the Department against employment of slaves in the general service, but then cited another regulation, that not more than one-twentieth part of the crew of any vessel is allowed to consist of Negroes. It is believed that the number is generally far within this proportion. Even though the Navy was hesitant to account for the use of slaves, a subsequent investigation revealed that the Treasury Department\u27s revenue-boat service, which was under the jurisdiction of the Navy Department, used slave crewmen.1 When questioning was complete, the Navy only reluctantly disassociated itself\u27 from the leasing of slave labor.

Second moments in the generalized Gauss circle problem

The generalized Gauss circle problem concerns the lattice point discrepancy of large spheres. We study the Dirichlet series associated to P k ( n ) 2 , where P k ( n ) is the discrepancy between the volume of the k -dimensional sphere of radius √ n and the number of integer lattice points contained in that sphere. We prove asymptotics with improved power-saving error terms for smoothed sums, including ∑ P k ( n ) 2 e − n/X and the Laplace transform ∫ ∞ 0 P k ( t ) 2 e − t/X dt , in dimensions k ≥ 3. We also obtain main terms and power-saving error terms for the sharp sums ∑ n ≤ X P k ( n ) 2 , along with similar results for the sharp integral ∫ X 0 P 3 ( t ) 2 dt. This includes producing the first power-saving error term in mean square for the dimension-three Gauss circle problem

Arithmetic Progressions of Squares and Multiple Dirichlet Series

We study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple Dirichlet series has meromorphic continuation to $\mathbb{C}^2$ and use Tauberian methods to obtain counts for arithmetic progressions of squares and rational points on $x^2+y^2=2$.Comment: 31 pages, (now incorporating helpful comments