Systems of forms in many variables

Thesis

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)...

Expand abstract

Authors: Myerson, S

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Hardy-Littlewood method; Forms in many variables; Rational points; Algebraic varieties; Circle method; Quadratic forms
• Subjects: Number theory; Mathematics; Analytic number theory