Title page for ETD etd-11092007-204825


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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