Objetivo
This is a proposal for research at the interface of analytic number theory, automorphic forms and algebraic geometry. Motivated by fundamental conjectures in number theory, classical problems will be investigated in higher order situations: general number fields, automorphic forms on higher rank groups, the arithmetic of algebraic varieties of higher degree. In particular, I want to focus on
- computation of moments of L-function of degree 3 and higher with applications to subconvexity and/or non-vanishing, as well as subconvexity for multiple L-functions;
- bounds for sup-norms of cusp forms on various spaces and equidistribution of Hecke correspondences;
- automorphic forms on higher rank groups and general number fields, in particular new bounds towards the Ramanujan conjecture;
- a proof of Manin's conjecture for a certain class of singular algebraic varieties.
The underlying methods are closely related; for example, rational points on algebraic varieties
will be counted by a multiple L-series technique.
Ámbito científico
Convocatoria de propuestas
ERC-2010-StG_20091028
Consulte otros proyectos de esta convocatoria
Régimen de financiación
ERC-SG - ERC Starting GrantInstitución de acogida
37073 Gottingen
Alemania