English
Algebraic and transcendental formulas for the smallest parts function
Post-edited
Auteurs : Ahlgren, Scott (Auteur de la Conférence)
CIRM (Editeur )
11F37 - Forms of half-integer weight; nonholomorphic modular forms
11P82 - Analytic theory of partitions
CIRM (Editeur )
Résumé :
We study the smallest parts function introduced by Andrews. The associated generating function forms a component of a natural mock modular form of weight 3/2 whose shadow is the Dedekind eta function. We obtain an exact formula and an algebraic formula for each value of the smallest parts function; these are analogues of the formulas of Rademacher and Bruinier-Ono for the ordinary partition function. The convergence of our expression is non-trivial; the proof relies on power savings estimates for weighted sums of generalized Kloosterman sums which follow from spectral methods.
Codes MSC : 11F37 - Forms of half-integer weight; nonholomorphic modular forms
11P82 - Analytic theory of partitions
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 18/06/15 Date de captation : 26/05/15 Sous collection : Research talks arXiv category : Number Theory Domaine : Number Theory Format : QuickTime (.mov) Durée : 00:42:44 Audience : Researchers Download : https://videos.cirm-math.fr/2015-05-26_Ahlgren.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Automorphic forms: advances and applications / Formes automorphes: avancées et applicationsOrganisateurs de la rencontre : Bringmann, Kathrin ; Lovejoy, Jérémy ; Richter, Olav Dates : 25/05/15 - 29/05/15 Année de la rencontre : 2015 URL Congrès : http://conferences.cirm-math.fr/1108.html
Données de citation
DOI : 10.24350/CIRM.V.18767903Citer cette vidéo: Ahlgren, Scott (2015). Algebraic and transcendental formulas for the smallest parts function. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18767903 URI : http://dx.doi.org/10.24350/CIRM.V.18767903 |
Bibliographie
- Ahlgren, S., & Andersen, N. (2015). Algebraic and transcendental formulas for the smallest parts function.
