Breadcrumb

Diophantine equations via the circle method

Supervisor: Tim Browning

Theme: Number Theory

The Hardy-Littlwood circle method is a remarkably effective tool in analytic number theory for deciding whether or not suitable families of Diophantine equations admit integer solutions. Despite many successes there remain many interesting problems left to tackle. For example, given a cubic polynomial equation f=0 in many variables, is it possible to produce a search bound for the size of the least integer solution in terms of the size of the coefficients of f?


Publications

  • Analytic methods for Diophantine equations and Diophantine inequalities (2005)
    H. Davenport
    Editors: T.D. Browning
    Publisher: Cambridge University Press