Analytic Number Theory: Higher Order Structures

Ziel

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.

Wissenschaftliches Gebiet

Finanzierungsplan

ERC-SG - ERC Starting Grant

Gastgebende Einrichtung

GEORG-AUGUST-UNIVERSITAT GOTTINGEN STIFTUNG OFFENTLICHEN RECHTS

EU-Beitrag

€ 1 004 000,00

Adresse

WILHELMSPLATZ 1
37073 Gottingen
Deutschland

Region

Niedersachsen Braunschweig Göttingen

Aktivitätstyp

Higher or Secondary Education Establishments

Hauptforscher

Valentin Blomer (Prof.)

Kontakt Verwaltung

Nadja Daghbouche (Ms.)

Links

Die Organisation kontaktieren Website

Gesamtkosten

Keine Daten

Begünstigte (1)