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1.
Everhart, Lance M.
On generators of Hilbert modular groups of totally *real* number * fields*.

Degree: 2016, NC Docks

URL: http://libres.uncg.edu/ir/uncg/f/Everhart_uncg_0154M_11992.pdf

In this paper we report the beginnings of the computations and tabulations of the generators of \PSL_{2}(\OK), where \OK is the maximal order of a real field of degree n=[K:\QQ]. We discuss methods of obtaining generators in order to calculate the values of invariants of the congruence subgroups. [This text field cannot display some of the mathematical formatting used in this abstract. To see the correctly formatted abstract, please click on the PDF below.]

Subjects/Keywords: Hilbert modules; Modular groups; Quadratic fields; Numbers, Real

Record Details Similar Records

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

APA (6^{th} Edition):

Everhart, L. M. (2016). On generators of Hilbert modular groups of totally real number fields. (Thesis). NC Docks. Retrieved from http://libres.uncg.edu/ir/uncg/f/Everhart_uncg_0154M_11992.pdf

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

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

Everhart, Lance M. “On generators of Hilbert modular groups of totally real number fields.” 2016. Thesis, NC Docks. Accessed July 15, 2020. http://libres.uncg.edu/ir/uncg/f/Everhart_uncg_0154M_11992.pdf.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Everhart, Lance M. “On generators of Hilbert modular groups of totally real number fields.” 2016. Web. 15 Jul 2020.

Vancouver:

Everhart LM. On generators of Hilbert modular groups of totally real number fields. [Internet] [Thesis]. NC Docks; 2016. [cited 2020 Jul 15]. Available from: http://libres.uncg.edu/ir/uncg/f/Everhart_uncg_0154M_11992.pdf.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Everhart LM. On generators of Hilbert modular groups of totally real number fields. [Thesis]. NC Docks; 2016. Available from: http://libres.uncg.edu/ir/uncg/f/Everhart_uncg_0154M_11992.pdf

Not specified: Masters Thesis or Doctoral Dissertation

University of Toronto

2.
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

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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