THE ASYMPTOTIC DISTRIBUTION OF TRACES OF WEAK MAASS FORMS

THE ASYMPTOTIC DISTRIBUTION OF TRACES OF WEAK MAASS FORMS

We give an asymptotic formula with a power saving error term for traces of CM values of a generic class of weak Maass forms. We apply this result to study the asymptotic distribution of several arithmetic functions, including the partition function, the Andrews smallest parts function, and the coeff...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematika 2021-10, Vol.67 (4), p.739-787
Hauptverfasser: Khaochim, Narissara, Masri, Riad, Tsai, Wei‐Lun
Format: Artikel
Sprache:eng
Schlagworte:
11F30
11P82
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We give an asymptotic formula with a power saving error term for traces of CM values of a generic class of weak Maass forms. We apply this result to study the asymptotic distribution of several arithmetic functions, including the partition function, the Andrews smallest parts function, and the coefficients of Ramanujan's mock theta function f(q).
ISSN:0025-5793
2041-7942
DOI:10.1112/mtk.12097