Identifier
etd-11092007-204825
Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
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.
Date
2007
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
Kim, Heon, "Sign Ambiguities of Gaussian Sums" (2007). LSU Doctoral Dissertations. 633.
https://repository.lsu.edu/gradschool_dissertations/633
Committee Chair
Helena Verrill
DOI
10.31390/gradschool_dissertations.633