Distribution and Correlation of Homogeneous and Random Forms

• Applicants: Professor Dr. Valentin Blomer; Professor Dr. Jörg Brüdern; Professor Dr. Friedrich Götze
• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 462335009

The study of Diophantine inequalities for indefinite homogeneous forms with integral or real coefficients is a classical question in analytic number theory. Starting with quadratic forms, we would like to establish bounds for the size of a non-trivial solution of such Diophantine inequalities, improving previous known results. Many questions in this area are expected to be challenging, but one could hope for definite answers at least for randomized forms. This naturally leads to statistical questions about zeros of random polynomials, value distribution of random forms, and averaged mean-value estimates, as well as the distribution of zeros for special classes of random zeta functions. The problems are interdisciplinary in nature combining analytic, probabilistic, Diophantine and automorphic techniques, which have shown to be successful in answering basic questions. The principal investigators have been active in these areas for a long time and therefore the combined background and experience should lead to further insights.

• DFG Programme: Research Grants
• Co-Investigator: Dr. Paul Buterus