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Aspects of x + y - z = 1 in positive characteristic

Leitner, Dominik. Aspects of x + y - z = 1 in positive characteristic. 2013, PhD Thesis, University of Basel, Faculty of Science.

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Official URL: http://edoc.unibas.ch/diss/DissB_10346

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Abstract

In the present thesis we focus on how to solve the equation x+y-z=1 completely in unknowns x,y,z chosen from the group G generated by t and 1-t in the function field F(t), where F is the field with p elements. The general theory is well-understood but there are rather few examples. Here we find at most 243 (so independent of p) families of solutions parametrized by (at most) a pair of prime-power exponents; these correspond to two independent actions of Frobenius. We also indicate how to go further by finding all solutions in the radical of G in the algebraic closure of F(t).
Advisors:Masser, David
Committee Members:Voloch, Felipe
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Zahlentheorie (Masser)
Item Type:Thesis
Thesis no:10346
Bibsysno:Link to catalogue
Number of Pages:71 Bl.
Language:English
Identification Number:
Last Modified:30 Jun 2016 10:52
Deposited On:07 May 2013 10:17

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