Evaluating convolution sums of the divisor function by quasimodular forms

Emmanuel Royer

doi:10.1142/S1793042107000924

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Evaluating convolution sums of the divisor function by quasimodular forms

Journal article

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Peer reviewed

Evaluating convolution sums of the divisor function by quasimodular forms

Emmanuel Royer

International Journal of Number Theory, Vol.3(2), pp.Page: 231 - 261

06/2007

DOI: https://doi.org/10.1142/S1793042107000924

Abstract

quasimodular form

divisor sum

arithmetical identities

11A25 11F11 11F25 11F20

We provide a systematic method to compute arithmetic sums including some previously computed by Alaca, Alaca, Besge, Cheng, Glaisher, Huard, Lahiri, Lemire, Melfi, Ou, Ramanujan, Spearman and Williams. Our method is based on quasimodular forms. This extension of modular forms has been constructed by Kaneko and Zagier.

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Title: Evaluating convolution sums of the divisor function by quasimodular forms
Creators - without role: Emmanuel Royer - Université de Montpellier, Institut Montpelliérain Alexander Grothendieck - IMAG
Publication Details: International Journal of Number Theory, Vol.3(2), pp.Page: 231 - 261
Identifiers: 9945946409311
Academic Unit: Institut Montpelliérain Alexander Grothendieck - IMAG
Language: English
Resource Type: Journal article
Local Fields: hal-00012320