CORDIS Project
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This project explores advanced topics in analytic number theory, focusing on the circle method, character sums, and quadratic forms. It aims to develop new mathematical techniques to address complex problems, including prime value attainment by quadratic forms and improvements in harmonic analysis.
This proposal investigates a series of problems in analytic number theory linked by the themes of the circle method, character sums, and quadratic forms.
The first set of objectives, for the circle method, proposes innovative extensions of Kloosterman refinements.
In particular we propose a novel two-dimensional Kloosterman refinement, the first of its kind, with impact on questions such as whether two quadratic forms must simultaneously attain prime values.
Additionally, we propose to develop f…
THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
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