Advanced search options

Sorted by: relevance · author · university · date | New search

You searched for `subject:(Binary Quadratic Fields)`

.
Showing records 1 – 2 of
2 total matches.

▼ Search Limiters

University of Toronto

1.
Dahl, Alexander Oswald.
On Moments of Class Numbers of Real *Quadratic* * Fields*.

Degree: 2010, University of Toronto

URL: http://hdl.handle.net/1807/24553

Class numbers of algebraic number fields are central invariants. Once the underlying field has an infinite unit group they behave very irregularly due to a non-trivial regulator. This phenomenon occurs already in the simplest case of real quadratic number fields of which very little is known. Hooley derived a conjectural formula for the average of class numbers of real quadratic fields. In this thesis we extend his methods to obtain conjectural formulae and bounds for any moment, i.e., the average of an arbitrary real power of class numbers. Our formulae and bounds are based on similar (quite reasonable) assumptions of Hooley's work. In the final chapter we consider the case of the -1 power from a numerical point of view and develop an efficient algorithm to compute the average for the -1 class number power without computing class numbers.

MAST

Subjects/Keywords: analytic number theory; real quadratic fields; binary quadratic forms; class group moments; 0405

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Dahl, A. O. (2010). On Moments of Class Numbers of Real Quadratic Fields. (Masters Thesis). University of Toronto. Retrieved from http://hdl.handle.net/1807/24553

Chicago Manual of Style (16^{th} Edition):

Dahl, Alexander Oswald. “On Moments of Class Numbers of Real Quadratic Fields.” 2010. Masters Thesis, University of Toronto. Accessed July 15, 2020. http://hdl.handle.net/1807/24553.

MLA Handbook (7^{th} Edition):

Dahl, Alexander Oswald. “On Moments of Class Numbers of Real Quadratic Fields.” 2010. Web. 15 Jul 2020.

Vancouver:

Dahl AO. On Moments of Class Numbers of Real Quadratic Fields. [Internet] [Masters thesis]. University of Toronto; 2010. [cited 2020 Jul 15]. Available from: http://hdl.handle.net/1807/24553.

Council of Science Editors:

Dahl AO. On Moments of Class Numbers of Real Quadratic Fields. [Masters Thesis]. University of Toronto; 2010. Available from: http://hdl.handle.net/1807/24553

Virginia Tech

2.
Miller, Nicole Renee.
The Structure of the Class Group of Imaginary *Quadratic* * Fields*.

Degree: MS, Mathematics, 2005, Virginia Tech

URL: http://hdl.handle.net/10919/32572

Let Q(√{-d}) be an imaginary quadratic field with
discriminant Δ. We use the isomorphism between the ideal
class groups of the field and the equivalence classes of binary
quadratic forms to find the structure of the class group. We
determine the structure by combining two of Shanks' algorithms [7,
8]. We utilize this method to find fields with cyclic factors that
have order a large power of 2, or fields with class groups of high
5-ranks or high 7-ranks.
*Advisors/Committee Members: Parry, Charles J. (committeechair), Haskell, Peter E. (committee member), Brown, Ezra A. (committee member).*

Subjects/Keywords: 7-rank; 5-rank; Positive Definite Forms; Genera; Class Group; Binary Quadratic Fields

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Miller, N. R. (2005). The Structure of the Class Group of Imaginary Quadratic Fields. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/32572

Chicago Manual of Style (16^{th} Edition):

Miller, Nicole Renee. “The Structure of the Class Group of Imaginary Quadratic Fields.” 2005. Masters Thesis, Virginia Tech. Accessed July 15, 2020. http://hdl.handle.net/10919/32572.

MLA Handbook (7^{th} Edition):

Miller, Nicole Renee. “The Structure of the Class Group of Imaginary Quadratic Fields.” 2005. Web. 15 Jul 2020.

Vancouver:

Miller NR. The Structure of the Class Group of Imaginary Quadratic Fields. [Internet] [Masters thesis]. Virginia Tech; 2005. [cited 2020 Jul 15]. Available from: http://hdl.handle.net/10919/32572.

Council of Science Editors:

Miller NR. The Structure of the Class Group of Imaginary Quadratic Fields. [Masters Thesis]. Virginia Tech; 2005. Available from: http://hdl.handle.net/10919/32572