Gregory P. Dresden

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The cyclotomic polynomials n for n = 1, 2, 3,. .. (familiar to every student of algebra) are the minimal polynomials for the primitive nth roots of unity: n (x) = (k,n)=1 x − e 2πik/n. Clearly n has degree φ(n), where φ signifies Euler's totient function. These monic polynomials can be defined recursively as 1 (x) = x − 1 and i|n i (x) = x n − 1 for n > 1.(More)
Acknowledgments I would like to thank my committee members, Gregory Dresden, Fer-nando Rodriguez-Villegas, John Tate and Felipe Voloch, for reviewing this dissertation and helping to make it complete. In particular, I thank Fernando Rodriguez-Villegas as well as John Garza for their ideas that inspired me to prove the results that appear here. I also thank(More)
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