Analytic Number Theory: Higher Order Structures

Obiettivo

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.

Campo scientifico

Meccanismo di finanziamento

ERC-SG - ERC Starting Grant

Istituzione ospitante

GEORG-AUGUST-UNIVERSITAT GOTTINGEN STIFTUNG OFFENTLICHEN RECHTS

Contributo UE

€ 1 004 000,00

Indirizzo

WILHELMSPLATZ 1
37073 Gottingen
Germania

Regione

Niedersachsen Braunschweig Göttingen

Tipo di attività

Higher or Secondary Education Establishments

Ricercatore principale

Valentin Blomer (Prof.)

Contatto amministrativo

Nadja Daghbouche (Ms.)

Collegamenti

Contatta l’organizzazione Sito web

Costo totale

Nessun dato

Beneficiari (1)