Type of Document	Dissertation
Author	Kim, Heon
Author's Email Address	hkim@math.lsu.edu
URN	etd-11092007-204825
Title	Sign Ambiguities of Gaussian Sums
Degree	Doctor of Philosophy (Ph.D.)
Department	Mathematics
Advisory Committee	Advisor Name Title Helena Verrill Committee Chair Charles Delzell Committee Member Padmanabhan Committee Member Richard Litherland Committee Member Robert Perlis Committee Member Martin Feldman Dean's Representative
Keywords	Gauss sum sign ambiguity
Date of Defense	2007-10-26
Availability	unrestricted
Abstract In 1934, two kinds of multiplicative relations, extit{norm and Davenport-Hasse} relations, between Gaussian sums, were known. In 1964, H. Hasse conjectured that the norm and Davenport-Hasse relations are the only multiplicative relations connecting the Gaussian sums over $mathbb F_p$. However, in 1966, K. Yamamoto provided a simple counterexample disproving the conjecture when Gaussian sums are considered as numbers. This counterexample was a new type of multiplicative relation, called a {it sign ambiguity} (see Definition ef{defi:of_sign_ambi}), involving a $pm$ sign not connected to elementary properties of Gauss sums. In Chapter $5$, we provide an explicit product formula giving an infinite class of new sign ambiguities and we resolve the ambiguous sign by using the Stickelberger's theorem.
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