Objectif 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 varietieswill be counted by a multiple L-series technique. Champ scientifique natural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsarithmeticsL-functionsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Thème(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Appel à propositions ERC-2010-StG_20091028 Voir d’autres projets de cet appel Régime de financement ERC-SG - ERC Starting Grant Institution d’accueil GEORG-AUGUST-UNIVERSITAT GOTTINGEN STIFTUNG OFFENTLICHEN RECHTS Contribution de l’UE € 1 004 000,00 Adresse WILHELMSPLATZ 1 37073 Gottingen Allemagne Voir sur la carte Région Niedersachsen Braunschweig Göttingen Type d’activité Higher or Secondary Education Establishments Chercheur principal Valentin Blomer (Prof.) Contact administratif Nadja Daghbouche (Ms.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution de l’UE Tout développer Tout réduire GEORG-AUGUST-UNIVERSITAT GOTTINGEN STIFTUNG OFFENTLICHEN RECHTS Allemagne Contribution de l’UE € 1 004 000,00 Adresse WILHELMSPLATZ 1 37073 Gottingen Voir sur la carte Région Niedersachsen Braunschweig Göttingen Type d’activité Higher or Secondary Education Establishments Chercheur principal Valentin Blomer (Prof.) Contact administratif Nadja Daghbouche (Ms.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée