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ID 54714
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Author
Ramakrishhan, B. Harish-Chandra Research Institute
Sahu, Brundaban School of Mathematical Sciences National Institute of Science Education and Research
Abstract
In this note, we evaluate certain convolution sums and make some remarks about the Fourier coefficients of cusp forms of weight 4 for Γ0(12). We express the normalized newform of weight 4 on Γ0(12) as a linear combination of the (quasimodular) Eisenstein series (of weight 2) E2(dz), d|12 and their derivatives. Now, by comparing the work of Alaca-Alaca-Williams [1] with our results, as a consequence, we express the coefficients c1,12(n) and c3,4(n) that appear in [1, Eqs.(2.7) and (2.12)] in terms of linear combination of the Fourier coefficients of newforms of weight 4 on Γ0(6) and Γ0(12). The properties of c1,12(n) and c3,4(n) that are derived in [1] now follow from the properties of the Fourier coefficients of the newforms mentioned above. We also express the newforms as a linear combination of certain eta-quotients and obtain an identity involving eta-quotients.
Keywords
convolution sums of the divisor function
Fourier coeffificients
newforms of integral weight
Published Date
2017-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume59
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
71
End Page
79
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
Official Url
http://www.math.okayama-u.ac.jp/mjou/
language
英語
Copyright Holders
Copyright©2017 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol59/iss1/5
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