Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

You searched for +publisher:"University of Illinois – Chicago" +contributor:("Cojocaru, Alina Carmen"). One record found.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters

1. Shulman, Andrew. Elementary divisors of reductions of generic Drinfeld modules.

Degree: 2012, University of Illinois – Chicago

Let q be a power of an odd prime, A := Fq[T], and k := Fq(T). Let ψ be a Drinfeld A- module over a fi nite extension K of k of rank r  ≥  2. Let \wp be a prime of K, of good reduction for ψ, \F\wp the residue fi eld at \wp, and consider the reduced Drinfeld A-module ψ \otimes \wp over \F\wp. The A-module action of ψ \otimes \wp on \F\wp, denote \F\wp, makes \F\wp isomorphic, as an A-module, to A / d1,\wp(ψ)A  ×  …  ×  A / dr,\wp(ψ) A for uniquely determined monic polynomials d1,\wp(ψ),…,dr,\wp(ψ), depending on ψ and \wp, such that d1,\wp(ψ) | … | dr,\wp(ψ). The elements d1,\wp(ψ),…,dr,\wp(ψ) are called the elementary divisors of ψ modulo \wp. In this thesis, we study the growth of the largest elementary divisor, dr,\wp(ψ), as the prime \wp varies, in analogy with a result by W. Duke pertaining to elliptic curves. We also consider the distribution of the smallest elementary divisor, d1,\wp(ψ), again as \wp varies, in analogy with work started by J.-P. Serre related to Lang and Trotter's elliptic curve formulation of Artin's primitive root conjecture. One of our main results is that for a density 1 of primes \wp of K, the infinity norm of dr,\wp(ψ) is as large as possible. More precisely, we show that for any function f de fined on the primes of K with values in A such that f grows very slowly as the degree of the primes in K increases to infinity, then almost all primes \wp of K satisfy |dr,\wp(ψ)|\ifnty > \frac{|\wp|}{|f(\wp)|. Advisors/Committee Members: Cojocaru, Alina Carmen (advisor), Coskun, Izzet (committee member), Popa, Mihnea (committee member), Talkoo-Bighash, Ramin (committee member), Zieve, Michael (committee member).

Subjects/Keywords: Drinfeld modules; elliptic curves; reduction; elementary divisors

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

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

APA (6th Edition):

Shulman, A. (2012). Elementary divisors of reductions of generic Drinfeld modules. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/8268

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Shulman, Andrew. “Elementary divisors of reductions of generic Drinfeld modules.” 2012. Thesis, University of Illinois – Chicago. Accessed July 12, 2020. http://hdl.handle.net/10027/8268.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Shulman, Andrew. “Elementary divisors of reductions of generic Drinfeld modules.” 2012. Web. 12 Jul 2020.

Vancouver:

Shulman A. Elementary divisors of reductions of generic Drinfeld modules. [Internet] [Thesis]. University of Illinois – Chicago; 2012. [cited 2020 Jul 12]. Available from: http://hdl.handle.net/10027/8268.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Shulman A. Elementary divisors of reductions of generic Drinfeld modules. [Thesis]. University of Illinois – Chicago; 2012. Available from: http://hdl.handle.net/10027/8268

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.