Sign Ambiguities of Gaussian Sums

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.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2007

Author dc:creator

• Kim, Heon

• Gauss sum
• sign ambiguity

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-11092007-204825
https://repository.lsu.edu/gradschool_dissertations/633

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-1632