Explicit multiplicative relations between Gauss sums

Identifier

etd-0708102-134248

Author

Brian J. Murray, Louisiana State University and Agricultural and Mechanical CollegeFollow

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

H.Hasse conjectured that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit product formula giving an infinite class of new sign ambiguities and resolve the ambiguous sign in terms of the order of the ideal class of quadratic primes.

Date

2002

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Recommended Citation

Murray, Brian J., "Explicit multiplicative relations between Gauss sums" (2002). LSU Doctoral Dissertations. 757.
https://repository.lsu.edu/gradschool_dissertations/757

Committee Chair

Paul van Wamelen

DOI

10.31390/gradschool_dissertations.757