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ID 54714
フルテキストURL
著者
Ramakrishhan, B. Harish-Chandra Research Institute
Sahu, Brundaban School of Mathematical Sciences National Institute of Science Education and Research
抄録
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.
キーワード
convolution sums of the divisor function
Fourier coeffificients
newforms of integral weight
発行日
2017-01
出版物タイトル
Mathematical Journal of Okayama University
59巻
1号
出版者
Department of Mathematics, Faculty of Science, Okayama University
開始ページ
71
終了ページ
79
ISSN
0030-1566
NCID
AA00723502
資料タイプ
学術雑誌論文
オフィシャル URL
http://www.math.okayama-u.ac.jp/mjou/
言語
English
著作権者
Copyright©2017 by the Editorial Board of Mathematical Journal of Okayama University
論文のバージョン
publisher
査読
有り
Submission Path
mjou/vol59/iss1/5