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Full-Text Articles in Physical Sciences and Mathematics
On Cyclotomic Primality Tests, Thomas Francis Boucher
On Cyclotomic Primality Tests, Thomas Francis Boucher
Masters Theses
In 1980, L. Adleman, C. Pomerance, and R. Rumely invented the first cyclotomicprimality test, and shortly after, in 1981, a simplified and more efficient versionwas presented by H.W. Lenstra for the Bourbaki Seminar. Later, in 2008, ReneSchoof presented an updated version of Lenstra's primality test. This thesis presents adetailed description of the cyclotomic primality test as described by Schoof, along withsuggestions for implementation. The cornerstone of the test is a prime congruencerelation similar to Fermat's \little theorem" that involves Gauss or Jacobi sumscalculated over cyclotomic fields. The algorithm runs in very nearly polynomial time.This primality test is currently one of …
On The Behavior Of The Asymptotics Of Robertson-Walker Cosmologies As A Function Of The Cosmological Constant, Noah Thomas Schaefferkoetter
On The Behavior Of The Asymptotics Of Robertson-Walker Cosmologies As A Function Of The Cosmological Constant, Noah Thomas Schaefferkoetter
Masters Theses
An analysis of the Einstein Field Equations within a Robertson-Walker Cosmology. More specifically, what values of the cosmological constant will result in a Big Bang.