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Thesis

Systems of forms in many variables

Abstract:

We consider systems of polynomial equations and inequalities to be solved in integers. By applying the circle method, when the number of variables is large and the system is geometrically well-behaved we give an asymptotic estimate for the number of solutions of bounded size.

In the case of R homogeneous equations having the same degree d, a classic theorem of Birch provides such an estimate provided the number of variables is R(R+1)(d-1)...

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Department:
Georg-August-Universität Göttingen

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Department:
University of Oxford
Role:
Supervisor
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Grant:
EP/J500495/1
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Project
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford

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