Leitner, Dominik. Aspects of x + y  z = 1 in positive characteristic. 2013, Doctoral 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+yz=1 completely in unknowns x,y,z chosen from the group G generated by t and 1t in the function field F(t), where F is the field with p elements. The general theory is wellunderstood 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 primepower 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) 
UniBasel Contributors:  Masser, David 
Item Type:  Thesis 
Thesis Subtype:  Doctoral Thesis 
Thesis no:  10346 
Thesis status:  Complete 
Number of Pages:  71 Bl. 
Language:  English 
Identification Number: 

Last Modified:  22 Jan 2018 15:51 
Deposited On:  07 May 2013 10:17 
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