Schmidt, Harry. Multiplication polynomials and relative ManinMumford. 2015, PhD Thesis, University of Basel, Faculty of Science.

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Official URL: http://edoc.unibas.ch/diss/DissB_11526
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Abstract
After the introduction we prove in chapter 2 that the resultant of the standard multiplication polynomials $A_n,B_n$ of an elliptic curve in the form $y^2 = x^3+ax+b$ is
$(16\Delta)^{{n^2(n^21) \over 6}}$, where $\Delta=(4a^3+27b^2)$ is the discriminant of the
curve. In the appendix we give an application to good reduction of an associated Latt\`es map. We also prove a similar result for the discriminant of the largest square free factor of $B_n$.
In the third chapter we prove a ManinMumford type result for additive extensions of elliptic families over the field of all complex numbers. We show in the appendix that there are finiteness consequences for Pell's equation over polynomial rings and integration in elementary terms. Our work can be made effective because we use counting results only for analytic curves.
In the third chapter we prove a ManinMumford type result for additive extensions of elliptic families over the field of all complex numbers. We show in the appendix that there are finiteness consequences for Pell's equation over polynomial rings and integration in elementary terms. Our work can be made effective because we use counting results only for analytic curves.
Advisors:  Masser, David William and Bertrand, Daniel 

Faculties and Departments:  05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Zahlentheorie (Masser) 
UniBasel Contributors:  Schmidt, Harry 
Item Type:  Thesis 
Thesis Subtype:  Doctoral Thesis 
Thesis no:  11526 
Thesis status:  Complete 
Bibsysno:  Link to catalogue 
Number of Pages:  1 OnlineRessource 
Language:  English 
Identification Number: 

Last Modified:  22 Jan 2018 15:52 
Deposited On:  04 Feb 2016 09:37 
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