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Algebraic and transcendental formulas for the smallest parts function

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Post-edited
Authors : Ahlgren, Scott (Author of the conference)
CIRM (Publisher )

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Dedekind eta function partition function smallest parts function formulas for the smallest parts function Kloosterman sums proof of algebraic formula proof of transcendental formula sums of Kloosterman sums
Abstract : 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.

MSC Codes :
11F37 - Forms of half-integer weight; nonholomorphic modular forms
 11P82 - Analytic theory of partitions
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 18/06/15
    Conference Date : 26/05/15
    Subseries : Research talks
    arXiv category : Number Theory
    Mathematical Area(s) : Number Theory
    Format : QuickTime (.mov) Video Time : 00:42:44
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2015-05-26_Ahlgren.mp4
Information on the Event

Event Title : Automorphic forms: advances and applications / Formes automorphes: avancées et applications
Event Organizers : Bringmann, Kathrin ; Lovejoy, Jérémy ; Richter, Olav
Dates : 25/05/15 - 29/05/15
Event Year : 2015
Event URL : http://conferences.cirm-math.fr/1108.html

Citation Data

DOI : 10.24350/CIRM.V.18767903
Cite this video as: 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

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